Comparative Naval Architecture of Modern Foreign Submarines

II... F.E = p 62COMPARATIVE NAVAL ARCHITECTURE OF MODERN

FOREIGN SUBMARINES

* In)Nby

(qi John K. Stenard, LT, USN00S.B. Mechanical Engineering, Massachusetts Institute ofN Technology, May 1980

SUBMITTED TO THE DEPARTMENT OF OCEANENGINEERING IN PARTIAL FULFILLMENT OF THE D T IC

REQUIREMENTS FOR THE DEGREE OF ELECTEMASTER OF SCIENCE N V2 3-

at the UiMASSACHUSETTS INSTITUTE OF TECHNOLOGY C010

May 1988

Copyright (c) 1988 John K. Stenard,The author grants to the Massachusetts Institute of Technology

and to the United States Government and its Agenciesthe right to copy this document in whole or in part.

Signature of AuthorDepartment of Ocean Engineering

May 27, 1988

Certified by l _.Professor Paul E. Sullivan

Thesis Supervisor

Accepted by i~K~KaProfessor A. Douglas Carmichael _

, R!eseor of Power Engineering,Chairman, Department Committee on Graduate Students

%g I Ioqq

COMPARATIVE NAVAL ARCHITECTURE OF MODERNFOREIGN SUBMARINES

by

John K. Stenard, LT, USN

Submitted to the Department of Ocean Engineering on May 27, 1988 Inpartial fulfillment of the requirements for the degree of Master of Science.

A- Abstract

A comparative design study of ten conventional and nuclear-powered fast attacksubmarines Is performed. Data sources are limited to those available In the openliterature. The analysis Is confined to those submarines which are of the greatestinterest and for which enough design Information Is available to conduct an adequatestudy. The data for each of the selected submarines is then parameterized, analyzed,and compared on the basis of design and military capabilities. The design philosophyand top level requirement of each submarine Is then Inferred from Its naval architectureand military capabilities. It Is concluded that automation of systems will allow a reductionof crew size, which then permits a larger battery and greater provision, fuel, andweapons loadouts. This will lead to greater combat effectiveness due to increasedrange, attack flexibility, speed, and weapons delivery potential. r- , ,,

2 . .. ... ..J .. ... . , , . .,,, . , A .I .2 J , . LC c.. -" - .- 4. .:-: , : . c, , .,-,, ! - / ,. ,.

'-I

iiD.',. - a"F -' .. " ,%. *!

BY

Dist

Thesis Supervisor: Professor Paul E. SullivanTitle: Associate Professor of Naval Architecture

-4-

Dedication

I dedicate this work to the hope that through the maintenance of a strong and effectivedefense by the United States, the world may avoid the waste and tragedy of armedconflict.

I extend my sincere appreciation and thanks to Professor Paul E. Sullivan, for educatingme on submarine design parameters, greatly assisting me In the extensive literaturesearch, and helping me define the-focus of this study, and whose patience during thepreparation of this document allowed me the freedom to be most effective.

My sincere thanks and admiration go to Harry Jackson, P.E., CAPT USN (Ret.) who,although known as a world-class expert on submarine design, extended to me an open-door policy to his home and personal library, and who provided mature engineeringguidance to me on several occasions as I developed the computer models of each of thesubmarines.

I wish to thank my parents, John D. and Ann E. Stenard, for always being loving andsupportive of me, my brothers and sisters, and my family.

My special thanks go to my wife, Amy, for being the love of my life, and for alwaysstanding by me, as my partner for life. She also contributed immeasureably to thequality of this document by proofreading it. My special thanks also to our two sons, JohnG. and James, for being such good little guys.

.5-

Table of Contents

Abstract 2Dedication 4Table of Contents 5List of Appendices 7List of Figures 8List of Tables 9Key to the Tables and Figures 111. INTRODUCTION 12

2. PURPOSE 14

3. SUMMARY OF SUBMARINES 154. DATA GATHERING AND SOURCES OF ERROR 27

4.1 Reference Convention 28

5. METHODOLOGY 29

6. VOLUME ANALYSIS 306.1 Volume Within the Pressure Hull 306.2 Volume External to Pressure Hull 316.3 Discussion 346.4 Volume Allocation 36

7. DISPLACEMENT AND WEIGHT ANALYSIS 397.1 Displacements 397.2 Functional Group Weights 42

8. MILITARY PERFORMANCE 468.1 Propulsion and Mobility 46

8.1.1 Required Shaft Horsepower 468.1.2 Fuel Endurance Range 528.1.3 Battery Endurance Range 548.1.4 Indiscretion Rate and Interval 578.1.5 Overall Endurance Range 57

8.2 Weapons Systems 608.2.1 Weapons Launching Systems 608.2.2 Torpedoes 698.2.3 Cruise Missiles 698.2.4 Mine Laying 708.2.5 Other Weapons Systems 70

8.3 Command. Control, Communication, and Information 718.3.1 Sonar 718.3.2 Periscopes 728.3.3 Radar 728.3.4 Electronic Surveillance Measures 75

.6-

8.3.5 External Communications 758.3.6 Automated Controls 76

8.4 Ship Support 768.5 Acoustic Countermeasures 778.6 Survivability and Damage Control 798.7 Escape and Rescue 82

9. COMPARATIVE NAVAL ARCHITECHTURE 849.1 Specific Volumes 84

9.1.1 Mobility 849.1.2 Weapons Systems 849.1.3 Command, Control, Communications, and Information 879.1.4 Ship Support 87

9.2 Mobility Weight/Installed Power 879.3 Overall Endurance Ranges at Six and Ten Knots 879.4 Battery Endurance Range 889.5 Indiscretion Rate and Interval 889.6 Escape Capability 919.7 Weapons Delivery Capabilities and Platform Efficiencies 91

9.7.1 Torpedoes 919.7.2 Cruise Missiles 969.7.3 Mines 98

9.8 Conclusions 98

10. AREAS FOR FURTHER STUDY 10010.1 Maneuvering Characteristics 10010.2 Weight Distribution 10010.3 Specific Fuel Consumption Increase at Snorkel 10010.4 Hull Strength Estimation 10110.5 Weapons and Sensors Capabilities 101

11. REFERENCES 102

*| .. & . .~. ~ .. . I !| i , , ..

.7.

List of Appendices

Appendix A: Geometry Calculations for Estimating Compartment Volumes

Appendix B: Numerical Evaluation of Submarine Wetted Surface Area

Appendix C: Calculation of Required Shaft Horspower Deeply Submerged

Appendix D: Calculation of Additional Shaft Horsepoer Required at Snorkel Depths

Appendix E: Endurance Range

Appendix F: Lead-Acid Battery Power and Energy Characteristics

Appendix G: Calculation of Battery Endurance Range

Appendix H: Calculation of Indiscretion Rate and Interval

Appendix I: Estimation of Weight Groups

Appendix J: Anaerobic Diesel Fuel/Air Loadout Calculation

Appendix K: Factors Affecting Crew Endurance

Appendix L: Factors Affecting Vulnerability and Survivability

Appendix M: Estimation of Hotel Electric Load

Appendix N: Diesel Engine Data

Appendix 0: Data on Other Modern Submarines

Appendix P: Diesel Engine Specific Fuel Consumption

Appendix Q: Calculation of Provision Ebndurance Range

Appendix R: Calculation of Prismatic Coefficient

-8-

List of Figures

7-1 Volumes of Functional Groups.

7-2 Volume Allocation Comparison.

8-1 Weights of Functional Groups.

8-1 Weight Allocation Comparison.

9-1 Shaft Horsepower Required. (Two sheets)

9-2 Ratio of SHP Required at Snorkel Depth to that Required When Deeply Submerged.

9-3 Snorkeling/Fuel Endurance Range.

9-4 Battery Endurance Range. (Two sheets)

9-5 Indiscretion Rate at 80% Depth of Discharge.

9-6 Indiscretion Interval at 80% Depth of Discharge.

9-7 Provision vs. Fuel Endurance Range. (Five sheets)

10-1 Endurance Range at 6 and 10 Kts.

10-2 Battery Endurance Ranges, At 6, 10, 18, and 25 Kts.

10-3 Indiscretion Rates at 6 and 10 Kts.

10-4 Indiscretion Intervals at 6 and 10 Kts.

10-5 Escape Capability Parameter Comparison.

10-6 Weapons Delivery Comparison 1: Torpedoes

10-7 Weapons Delivery Comparison 2: Cruise Missiles

10-8 Weapons Delivery Comparison 3: Mines

F-1 Available Battery Energy as a Function of Speed, 80% Depth of Discharge.

F-2 Battery Total Power Output at Various Speeds, 80% Depth of Discharge.

P-1 Diesel Engine Specific Fuel Consumption Generic Profile.

.9.

List of Tables

7-1 Functional group volumes calculated from measurement of reference pictures. (Two

sheets)

8-1 Displacements and functional group weights. (Two sheets)

9-1 Propulsion plant and other mobility group parameters. (Two sheets)

9-2 Weapons systems parameters. (Two sheets)

9-3 Command, Control, Communication, and Information Systems

9-4 Ship support systems parameters.

9-5 Countermeasure outfit.

9-6 Compartment measurements germane to damaged survivability.

9-7 Escape and rescue capabilities.

10-1 Comparison of performance and design parameters. (Two sheets)

A-1 Volume calculation tool "SECTOR3.WKI".

B-1 Numerical interpolation and surface integration spreadsheet "SPLINSUB.WK1".(Thirteen sheets)

B-2 Numerical Interpolation and surface integration spreadsheet "HERMFAST.WKI".(Thirteen sheets)

C-1 Calculated values of required shaft horsepower (SHP) as a function of speed. (Twosheets)

D-1 The calculated values of required shaft horsepower when operating at snorkeldepth. (Two sheets)

E-1 Calculated values of endurance range based upon bunker fuel loadout. (Twosheets)

F-1 Available energy from each submarine battery at several transit speeds. 80% depthof discharge. (Two sheets)

G-1 Calculated values of each submarine's endurance range on batteries alone. 80%depth of discharge. (Two sheets)

H-1 Calculated values of indiscretion rates at various speeds. (Two sheets)

-10.

H-2 Calculated values of indiscetion Interval as a function of submerged speed. (Twosheets)

N-1 Diesel engine and electric propulsion motor data.

0-1 Data on several other modem submarines, from the literature. (Five sheets)

P-1 Estimated diesel engine specific fuel consumption, as a function of speed. (Twosheets)

0-1 Provision endurance, In nautical miles, at various speeds.

R-1 Calculation of prismatic coefficient.

Key to the Tables and Figures

Number Submarine

#1 KILO

#2 WALRUS

#3 RUBIS

#4 BARBEL

#5 TYPE 2400

#6 TYPE 1700

#7 TYPE 2000

#8 SAURO

#9 VASTERGOTLAND

#10 MIDGET 100

-12.

Chapter 1

INTRODUCTION

The Introduction of the submarine added a new dimension to the conduct of naval

conflict; that of a potent undetected threat within striking distance. The ability of the

submarine to travel from place to place and observe events undetected usually gives to

the submarine the ability to attack first (or to decide not to attack) and has always been

Its greatest asset. The traditional weapon of the submarine has been the torpedo. which

because of its underwater attack mode is particularly damaging to surface ships.

Today, the ability of the submarine to remain undetected Is still its greatest asset.

Technical advances in hydrodynamics, propulsion plant design, and acoustic silencing

have made modem submarines more difficult to detect than ever. Similarly, the

firepower of the submarine has increased greatly due to technical advances in

submarine launched weapons systems.

Many nations include submarines as an Important part of their fleet. Several navies

consider their submarines to be their capital ships, and employ them for many peacetime

"ises. Some of the peacetime uses are oceanographic exploration and surveillance.

The primary wartime role of the submarine could be considered to be the same as it

always has been, that of interdiction of sea traffic lanes, but the methods of

accomplishing this task have been expanded. since most modem submarines are

capable of loading mines and encapsulated cruise missiles as well as torpedoes.

The mining capability allows a nation to restrict or deny the use of a port or seaway

choke-point to an adversary. This is a very important capability, and is possible for only

a submarine In many cases, since a submarine can conduct mining operations under

-13-

conditions Infeasible for aircraft or surface ships. In addition, the mining can be

conducted In a covert manner, which Is essential In this day of cruise missile shore

batteries.

The capability of a submarine to carry cruise missiles gives it the medium-range (50

nautical mile) stand-off attack mode against surface targets. This mode was previously

the province of only surface ships and attack aircraft. Long-range strategic nuclear

cruise missiles and rocket-propelled homing torpedoes have also been discussed and

are In development for attack submarine loadout.

The sophistication of modem torpedoes has increased their range, speed, probability of

hit, and overall lethality. While this thesis does not discuss weapons effects, it is

generally accepted that a subsurface explosion is much more damaging to a surface

ship than an equally-sized explosion In the superstructure. The weapon of choice for

attack submarines is still considered to be some variation of the torpedo.

This thesis focuses primarily upon basic mission capabilities such as number and type of

weapons carried, maximum speed, maximum mission length, submerged endurance

range, and indiscretion rate of diesel-electric submarines. One small nuclear-powered

craft is included for comparison. All of the submarines selected for analysis are "attack

boats", as opposed to strategic nuclear ballistic missile submarines,

Design data for the craft studied in this thesis is analyzed in a comparative technique.

which starts with a gross characteristics comparison. After gross differences are

identified, a detailed study of several aspects of the designs is undertaken. Emphasis is

placed upon identifying design differences, and on trying to establish the reason for

these differences.

IU

-14.

Chapter 2

PURPOSE

The purpose of this thesis is twofold:

(1). To determine the capability of each of the selected submarines in terms of primary

mission areas, which are generally of a military nature.

(2). To gain a greater understanding of naval architecture In general and submarine

design In particular.

-15-

Chapter 3

SUMMARY OF SUBMARINES

The literature search having been conducted, the below listed submarines have been

selected for Inclusion In the detailed analysis portion of this study. They are listed In

order of decreasing displacement. followed by the builder's name, country of origin, and

year the lead ship was launched.

(1) KILO (Komsomolsk Shipyard, Union of Soviet Socialist Republics, 1980).

(2) WALRUS (Rotterdamsche Droogdok Maatschappj B.V., The Netherlands, 1985)

(3) SSN RUBIS (Cherbourg Naval Dockyard. France, 1979).

(4) BARBEL (Portsmouth Naval Shipyard, United States, 1959).

(5) TYPE 2400 "UPHOLDER" (Vickers Shipbuilding and Engineering Ltd., Great Britain,

1986).

(6) TYPE 1700 (Thyssen Shipyard. Federal German Republic, 1982).

(7) TYPE 2000 (Ingenierkontor-Lubeck, Federal German Republic, 1983).

(8) SAURO (Fincantied Shipyard, Italy, 1979).

(9) VASTERGOTLAND (Kockums Shipyard, Sweden, 1986).

(10) MIDGET 100 (Sub Sea Oil Services of Micoped, Italy, 1984).

The BARBEL Class is included because it was the last diesel-electric submarine class to

be constructed by the United States. The KILO Class is included because of its interest

and widespread use among Communist Bloc and allied nations, and because it

represents a state-of-the-art Soviet diesel-electric submarine. The RUBIS. a small

nuclear-powered submarine, is included in the study to show the impact of its propulsion

plant. compared to other designs.

"7

.16-

The following pages summarize the gross attributes of the above selected submarine

classes.

-17-

ERemsemolsk ShipyardUnion of Soviet Socialist Republics1980

Submerged Displacement: 3200 Ltonsurface Displacoment: 2500 LtonStandard Disilacement: 1900 Lton (atimte)

Length: 229.6 ftSurfaced Draft: 23.0 ftDiameter: 29.5 ft

Complemnt: 55 Men.

Pime Mover Type: Diesel Engine/Storage DatteryDiesel/Alternator Capacity: 4480 KWMaJi Propulsion Motor Power: 4000 B1

Maximum Submerged Speed: 18 Xts (Calculated)Maximum Surface Speed: 12 Xts (Zstimate)Maximum Snorkel Speed: 10 Eta (ZEtimate)

Diving Depth: 300 meters (Estimate)

Overall Endurance Range at Six t t: 5760 HmOverall Endurance Range at Ten Ets: 9600 HmMaximm Mission Duration: 45 Days

Active Sonar.

Passive Sonar.

Array Sonar.Navigation Radar.Electronic Surveillance Gear.

Number of Torpedo Tubes: 8Number of Reloads Carried: 10

Cruise Missile Capable.May carry and launch a maximum of 18 SSN-21

Capable of Mnelaying.

Maximum Possible Number of MLnes Carried: 20

Not Capable of Delivering Swimrs. -

A

Rotterdamsche Droogdok Matschappij 3 .V.The Netherlands1965

Sumrged Displacment* 2600 LtonSurface Displaemnt: 2450 LtonStandard Displacmnt: 1900 Lten


Coplmnt: 50 Men.

Prime "over Type: Diesel EngIne/Storage BatteryDiesel/Alternator Capacity: 5170 XWMain Propulsion Motor Power: 5360 UP

Max-imium Submierged Speed: 20 XtsMaxim=m Surface Speed: 12 XtsMaximum Snorkel Speed: 12 Rts

Diving Depth: In excess of 300 meters.

Overall Endurance Range at Six Kta: 10000 HmOverall Endurance Range at Ton Kts: 7176 MMaximum Mission Duration: 70 Days

Active Sonar.Passive Sonar.Array Sonar.Navigation Radar.Zlectronic Surveillance Geer.


cruise Missile Capable.May carry and launch the Sub~arpoon.Max number Carried: 26

Can carry and emplace 40 mines.

Cherbourg Naval DockyardFrance1979

Submerged Displacment- 2670 LtonSurface Displacmnt: 2385 LtonStandard Displaement- 2250 Lton (Estimate)

Length: 236.5 ftSurfaced Draft: 21.0 ftDimter: 24.9 ft

Coilmnt: 9 Officers, 57 Enlisted Men

Prime mover Type: Nuclear Reactor,LIquid Metal Cooling

Prime Mover Power: 48,000 RI!main Propulsion motor Power: 10,000 EP

Maxi mum SBme rged Speed: 25 RtsMaxim=m Surface Speed: 20 Rto (Zst.)

Diving Depth: In excess of 300 motors.

Overall Endurance Range at Six Xts: 8640 MmOverall Endurance Range at Ten Kts: 14400 NmMaxm Mission Duration: 60 Days

Active Sonar.Passive Sonar.Array Sonar.Navigation Radar.Electronic Surveillance Gear.


Cruise Missile Capable.May carry a maxim- of 14 5)4-39 cruise missiles

Can carry and place 20 mines.

-20-

Port smouth Naval ShipyardUnited States1959 4

Submerged Displaceient: 2369 LtonSurface Dsplacmnt: 2315 LtonStandard Displacement: 2146 Lton

Length: 219.1 ftSurfaced Draft: 20 ftDiamter: 29 ft

Complmnt: 8 officers, 69 Znlisted.

Prime Mover Type: Diesel Znglno/Storage BatteryDiesel/Alternator Power: 3580 KWMain Propulsion Motor Power: 3150 HP

Maximum Submerged Speed: 18 Xts (Calculated)Maximum Surface Speed: 15 KtzMaximum Snorkel Speed: 10 Kto

Diving Depth: Xn excess of 120 mters.

Overall Indurance Range at Six Xts: 8640 NmOverall Enduranc* Range at Ten Xts: 9897 NO,Maximum Mission Duration: 60 Days



Cruise Missile Capable.May carry and launch the 12 Sub-Sarpoon.


Unknown if swimmwer capable.

-21-

TYPE 2400 "UPHOLDER"Vickers Shipbuilding 6Engineering Ltd.United Kingdom1L986

Submerged Displacmnt: 2400 Ltonsurf ace Displacmnt: 2188 LtonStandard Displacmnt: 1850 Lton

Length: 230.6 ftSurfaced Draft: 17.7ftDiameter: 25 ft

Complement: 7 Officers,13 CPO, 24 Enlisted. (44 Total)

Prime Mover Type: Diesel EngiLne/Storage BatteryPrime Hover Maxim=m Power- 3620 aPMain Propulsion Motor Power: 5360 HP

maximum Suba rged Speed: 20 RtsMaximum Surface Speed: 12 EtaMaximum Snorkel Speed: 10 Ets


Overall Endurance Range at Six Ets: 7056 "aOverall Endurance Range at Ton Eta: 5221 NmMaximum Mission Duration: 49 Days



Cruise Missile Capable.May carry and launch 12 Sub-Harpoon missiles.


Equipped with airlock for five combat swiamCor.

-22-

Type 1700Thyssmen Shipyardrederal German Republic1964

Submerged Displacment: 2350 Ltonsurface DIsplac ment: 2140 LtonStandard Displacement: 1760 Lton


Complement: 30-35 Man.

Prime Mover Type: Diesel Enqine/Storage BatteryDiesel Generator Maximum Power: 4400 RNmain Propulsion Mot~r Power: 9844 aP

Maximum Submerged Speed: 25 XtsMaximum Surf a,:e Speed: 15 KtsMaximum Snorkel Speed: 15 Rts


Overall Endurance Range at Six Xts: 10080 NmOverall Endurance Range at Ten Xts: 10736 MmMaximum Mi.ssion Duration: 70 day.



Not Cruise Missile Capable.

Can carry and emuplace 32 mines.

Not Capable of Delivering Swiumters.

-23-

TTPE 2000Ingeniourkontor- Lubeck

Federal German Republic1983

Sumierged Displacement: 3106 LtonSurface Displacement: 2820 LtonStandard Displacement: 2200 Lton

Length: 210.6 ftSurfaced Draft: 21 ftDiameter: 24.4 ft

Complement: 33 Men.

Prime Hover Type: Diesel Engine/Stoxaqe BatteryDiesel Generator Maximum Power: 3600 KWMain Propulsion Motor Power: 7500 HP

Maximum Submerged Speed: 25 KtsMaximum Surface Speed: 13 RtsMaximum Snorkel Speed: 15 Kts

Diving Depth:

Overall Endurance Range at Six Kts: 12651 NmOverall Endurance Range at Ton Kts: 9293 NmMaximum Mission Duration: Days

Number of Torpedo Tubes: aNumber of Reloads Carried: 18



Not Capable of Delivering Swimmers,

.24.

rincantieri ShipyardItaly1979

Submerged Displacmnt: 1660 LtonSurface Displacement: 1400 LtonStandard Displacement: 1280 Lton

Length* 192. ftSurfaced Draft: 17 ftDiameter: 22.4 ft

Complement: 35 Men.

Primes Mover Type: Diesel Enginet/Storage Battery

Diesel Generator Maximum Power: 2160 KW

main Propulsion Motor Power: 3216 NP Continuous4200 RP (Burst)

Maximm Submerged Speed: 19.3 XtsMaximum Surface Speed: 11 KtsMaximum Snorkel Speed: 11 Kts

Diving Depth: In excess of 300 moters.

overall Endurance Range at Six Kts: 6480 NutOverall Endurance Range at Ten Xts: 6891 NMMaximum Mission Duration: 45 Days

Active Sonar.Passive Sonar.Navigation Radar.Electronic Surveillance Gear.VLF Radio Receiver.

Number of Torpedo Tubes: 6

Number of Reloads Carried: 6

not Cruise Missile Capable.


Not Capable of Delivering Swimmers.

-25-

VASTURQOTLAND CLASSKockmso ShipyardSweden196

Submerged DIsplacinosnt: 1150 LtonSurface Displacement: 1070 LtonStandard Displacement: 990 Lton

Length: 159.1 ftSurfaced Draft: 17 ftDiameter: 20.3 ft

Complement: 21 Men.

prime Mover Type: Diesel Engine/Storage BatteryDiesel Generator Maximuzm Power: 2160 KWPrime Mover Maximum power: 2680 3?Main Propulsion Motor Power: 2537 RV

Maximum Submerged Speed: 20 XtsMaximum Surface Speed: 121 KtsMax-imum Snorkel Speed: 10 Kts (Estimate)


Overall Endurance Range at Six Rts: 3231 NmOverall Endurance Range at Ten Rts: 1956 MMaximum Mission Duration: 30 Days

Passive sonar.ElectroniLc Surveillance Gear.

Number of Torpedo Tubes: 6 Heavyweight tubes3 Lightweight tubes

Number of Reloads Carried: 6 Heavyweight

Not cruise missile capable.


May also carry mines in external belt.

Not Capable of Delivering Swizme.

-26-

MXDGET 100 "LWT 27-4"sub sea Oil Services of MicoperiItaly1984

Submer god Displacment: 136 Ltonsurface Diapacmnt: 120 Lton (Estimate)Standard Displacementz 100 Lton

Length: 88.9 ft (27.1 meters)Diameter: 10.3 ft

Couqlemnt: 12 (+ 4 combat ow-ime)

Prime Mover Type: Closed-Cycle DieselSmall battery Installed for stealth.

Main Propulsion Motor Power: 420 3PDiesel/Generator Total Power: 120 31

Maximm Sustained Subm~erged Speed: 16 KtsDoes Not Need to Snorkel.


Overall Endurance Range at Six Xts: 1345 NaOverall Endurance Range at Ten Kts: 819 NaMaximum MissiLon Duration: 14 Days

Active/Passive Sonar.Array Sonar.Navigation Radar.

Number of Torpedo Tubes: 4 (Lightweight)

Number of Reloads Carried: None (Nuzzle Loaded)


Twin 7.62mm Dock guns and Single 20ma Deck Gun.

Capable of Minelaying.Maximum Possible Number of Mines Carried: 4Variant carries two mine delivery vehicles with

10 x 600Kg mines.

-27-

Chapter 4

DATA GATHERING AND SOURCES OF ERROR

There were two methods of data acquisition for this study. The first type was a search of

the open literature for articles, advertisements, and manufacturer's brochures of interest.

The second data source was that gained by calculation or estimation of values directly or

indirectly from the data which could be gleaned from the open literature. Sensitive.

proprietary, or classified information, or information gained through such channels, must

be excluded from the thesis. Therefore, some of the data in this study is "second-

generation" data, calculated or estimated from available published data. This introduces

the possibility of error.

In the literature search It was found that some performance figures, such as maximum

speed and number of torpedo tubes, were almost always available, usually in Jane's

Fighting Ships. (17). Beyond these data elements, the sources were Incomplete or, in

some cases, contradictory of one another. One reason for some of the contradiction in

the literature is probably due to the inevitable unintentional misquote of some corporate

or government spokesperson. Literature sources are usually quite close to one another.

so that the error introduced was usually not of great significance. For example. a

submarine designed to accomodate sixty-two men could doubtlessly sustain a crew of

sixty-seven (albeit for a shorter mission duration). One othei possible source of

literature data discrepancy is that the authors of the articles may not all have the same

initial data with which to conduct their analyses. Articles in the literature, as opposed to

manufacturer's brochures. are authored by a certain group of naval architects and naval

ship analysts. each of which doubtlessly has his own set of empirical relations.

correlation coefficients, and rules of thumb with which to conduct his analyses. Even if

-28-

all of these naval architects were given the same Initial data on a given submarine, there

is bound to be a certain range of calculated and estimated secondary data values

resulting from each of them. Where conflicting values of data exist in the literature, a

notation is made, and the author's judgement is used to select the preferred value.

As a result of the problems with the data mentioned above, the accuracy of much of this

thesis Is probably not grater than ten-percent. This error comes from some things as

simple as being unable to measure submarine dimensions with extreme accuracy from

an isometric and only partially-exposed cutaway view in a magazine, to the fact that

errors will compound when used in calculations.

Care has been taken to limit discussion to obvious design features and differences

between ships. The magnitude of the error is, therefore, deemed acceptable for the

purpose of this analysis.

4.1 Reference Convention

In the data tables and figures included in this study, the sources of the information are

referenced in the following manner:

* Information from the literature is denoted by a number. in parentheses.which corresponds to the reference from which it was taken.

* Values calculated In the course of this study are unreferenced.

* Values or conditions which are estimated by the author, in the author's bestjudgement. are referenced by an "(e)" next to the entry.

* Values or conditions which are inapplicable to a calculation are designatedby "N/A".

.29.

Chapter 5

METHODOLOGY

The method by which this thesis was carried out Is straightforward, and consists of the

following:

(I). Acquisition of available data from open-literature sources.

(2). Calculation or estimation of neccessary data which is not readily available or which

could not be found.

(3). Parameterzation of each of the selected submarines according to reasonable

mathematical indices of description.

(4). Comparison of each of the submarines according to its indices of description.

Finally, an attempt is made to "reverse engineer" the design process of each submarine

in order to determine the nature of the top-level requirement.

-30-

Chapter 6

VOLUME ANALYSIS

6.1 Volume Within the Pressure Hull

The pressure hull volume distribution Is of prime Importance In the design of a

submarine. The pressure hull volume Is determined partly by the size of the payload,

but it must also contain and protect the propulsion plant, electronics, weapons. and

crew. The tradeoff In volume allocation between each of these areas determines, to an

extent, the performance capabilities of the submarine. The overall volume of the

pressure hull, and the allocation of that volume, give considerable insight into the design

philosophy of each submarine.

The pressure hull of most submarines is composed of sections of cylinders, cones, and

spheres. The pressure hull of the MIDGET 100 is one exception, since its pressure hull

has the same teardrop shape as its external envelope, rather than cylinders or cones.

The pressure hull total volume is readily calculated from the formulas of Appendix A.

provided a detailed reference picture of the vessel exists. The reference pictures of the

submarines in this study were of detail sufficient to allow calculation of pressure hull

volume to within five percent. Reference pictures were not available for KILO and TYPE

2000.

More difficult is the calculation of the volumes of the individual functional areas within the

pressure hull. The assignment of pressure hull volumes to each functional area. for the

purpose of this study, is defined below. Where two or more functional areas share the

same space, a judgement is made of the volume occupied by each function.

(1). Mobility. Includes the spaces housing all propulsion machinery. non-distributed

-31-

electric plant equipment, bow thrusters, steering gear, batteries, and Internal fuel tanks.

Also Includes trim and auxiliary ballast tanks, and HP air flasks.

(2). Weapons. Includes the volume of the torpedo tubes, handling gear, ejection and

launching equipment within the pressure hull, and the volume of the torpedo room.

excluding any volume used for berthing.

(3). Command, Control. Communication, and Information, (C31). Includes radio, sonar.

radar, electronic warfare, periscopes, computers, navigation center, and control rooms.

Also Includes (an arbitrary) forty percent of the air-conditioning plant.

(4). Ship Support. Includes berthing, me&.'Ing, galley, sanitary. and passageway space.

Also Includes all auxiliary machinery except that alloted to C31.

The calculated volumes of each functional group within the pressure hull are shown In

Table 7-1.

6.2 Volume External to Pressure Hull

The ballast tank volume Is calculated from the difference In the values of the submerged

and surfaced displacements. which In general can be found In the literature.

The free flood volume is assumed to be five-percent of the submerged volume. The

reference pictures of each submarine tend to confirm that the free flood volume is

concentrated primarily In the fairwater, around the bow sonar array and torpedo tubes.

and at the stem in the vicinity of the shaft.

The envelope volume of each submarine is estimated by summing the submerged

volume and the free flood volume.

The remaining volume external to the pressure hull is found by subtracting the ballast

tank volume and the pressure hull volume from the envelope volume. The other volume

-32-

SUBMARINE NAME

VOLUMES KILO WALRUS RUBIS BARBEL TYPE(in cubic feet) 2400

WITHIN PRESSURE HULL

MOBILITY VOL 33000 33527 48042 25630 37044WEAPONS VOL 10000 9281 10176 7290 6724C31 SYSTEMS VOL 11000 5900 5890 6701 9127SHIP SUPPORT VOL 14000 27752 15990 14562 11428

TOTAL: 68000 76460 80098 54183 64323

EXTERNAL TO PRESSURE HULL

BALLAST TANK VOL 24500 12250 9975 11340 8400OTHER SUBMRGD VOL 19500 9290 3377 26842 11277TOTL SUBMRGD VOL 112000 98000 93450 92365 84000ASSUMED FREEFLOOD 5600 4900 4672. 4618. 4200TOTAL ENVLPE VOL 117600 102900 98122 96983 88200

REFERENCE DRAWINGFOR MEASUREMENTS: (e) (18) (10) (35) (13)

Table 7-1: Functional group volumes calculated from measurement ofreference pictures. (Sheet one of two).

-33-

SUBMARINE NAME

VOLUMES TYPE TYPE SAURO VASTER- MIDGET(in cubic feet) 1700 2000 GOTLAND 100

WITHIN PRESSURE HULL

MOBILITY VOL 50021 44000 23775 17488 957WEAPONS VOL 5676 6000 8589 7092 405C31 SYSTEMS VOL 4806 5300 7290 4803 743SHIP SUPPORT VOL 10043 10000 9817 7564 1265

TOTAL: 70546 65300 49471 36947 3370

EXTERNAL TO PRESSURE HULL

BALLAST TANK VOL 7350 9310 6300 2450 420OTHER SUBMRGD VOL 4354 6940 2329 503 970TOTAL SUBMRGD VOL 82250 81550 58100 39900 4760ASSUMED FREEFLOOD 4112. 4078 2905 1995 238TOTAL ENVLPE VOL 86362 85628 61005 41895 4998

REFERENCE DRAWINGFOR MEASUREMENTS: (2) (e) (12) (36) (29)

Table 7-1: Functional group volumes calculated from measurement ofreference pictures. (Sheet two of two).

.34-

may be made up of structure, fuel tanks, high-pressure air flasks, conformal or traied

sonar arrays, periscopes and masts, snorkel, fittings, and special-purpose equipment.

Table 7-1 shows the calculated values of each submarine's main ballast tank and free

flood volume, other submerged volume, and the envelope volume.

6.3 Discussion

Figure 7-1 graphically depicts the actual measured and calculated volumes of each of

the functional groups, plus main ballast tank volume and other volume external to the

pressure hull, for each of the submarines. The volumes for KILO and TYPE 2000 are

estimated, since reference pictures were not available.

The first Item of Interest In Figure 7-1 is the variance in scale between the ten

submarines In this study. The largest boat, KILO, Is over twenty-three times the size of

the MIDGET 100, wfth the other submarines falling between those extremes. Since

Figure 7-1 displays each of the actual functional area volumes, It Is possible to compare

the sizes of each submarines' weapons area, or electronics/command suites by

inspection.

The C31 functional group volume is largest in the KILO of all the submarines. Though

the Installed electronic equipment aboard KILO is not thought to be any greater than that

Installed in the other submarines, Soviet electronics are probably more voluminous than

similar Western electronics because of the extensive use of vacuum tubes rather than

solid-state technology. The C31 volumes for the WALRUS, RUBIS. BARBEL. TYPE

'1700, TYPE 2000, and VASTERGOTLAND are nearly the same, even though the

vessels vary in submerged displacement by a factor of two from the smallest to the

largest. This demonstrates that the volume required to enclose sensor electronics and a

command center aboard an oceangoing submarine is not a strong function of the vessel

displacement.

-135-

'7 111

I.-C x .

4-A4

0n M~ r4

Ip pu Mn UO~q -L

Figure 7-1: Volumes of submarine functional groups.

-36-

Figure 7-1 shows the actual volumes of each of the functional groups, plus main ballast

and other external volume, for each submarine. Some values are Immedlatly noticed In

Figure 7-1, such as the large mobilty volumes for the RUBIS, TYPE 1700, and TYPE

2000, each of which has a large propulsion plant. In fact they have the three largest

Installed shaft horsepower plants of the submarines studied, and together have more

horsepower than the remaining seven combined. The TYPE 1700 and the TYPE 2000

have larger batteries than the others, and the RUBIS has a nuclear reactor contributing

to the volume. Also noticable are the small mobility volumes for the VASTERGOTLAND

and the MIDGET 100, each of which have less-powerful propulsion plants, and smaller

batteries than the others.

The BARBEL and KILO each have large non-ballast volumes external to the pressure

hull. The KILO has this volume because of Its double-hull, the BARBEL because of the

placement of large banana-shaped high-pressure air tanks between the pressure hull

and the hydrodynamic envelope.

The ship support volume of each submarine would be considered a function of the

complement, but each designer/builder has a different opinion of the habitability

standards required by a submarine crew. Appendix K discusses some factors affecting

crew endurance, not the least of which is volume-per-man within the pressure hull. The

large differences in ship support volume among the submarines does not correlate to the

variances In their complements. Chapter 10 discusses this in greater detail.

6.4 Volume Allocation

The allocation of volume In a submarine can indicate the functional groups which were

most important to its designer. Figure 7-2 shows the volume distribution of each

submarine. Note the high fraction of the volume dedicated to mobility in RUBIS, TYPE

1700, and TYPE 2000.

.37-

KILO and BARBEL have large non-ballast volumes external to the pressure hull,

because of their double-hull conmstruction. This volume Is proportionately large In

MIDGET 100 also, but it is due to the disproportionately large fairwater which cannot be

made smaller or It would be unusable.

WALRUS and MIDGET 100 have very high shlp support fractions. This was probably

planned In the case of WALRUS. because of Its long mission duration. For MIDGET

100, It Is unavoidable due to the scale effect of having the diameter of the vessel

comparable to the human body height.

C. XYV~ . 4§ ._ Z

'VI

LLr

ell 14 N

f Ui 1 CLI

AjwnxOAxO. ;c.%xPAuA *q *fJ...igure 7-2: Sumrn vouealoaincoprsn

.39-

Chapter 7

DISPLACEMENT AND WEIGHT ANALYSIS

7.1 Displacments

Each submarine may be described by three displacements:

1. Standard displacement Is the displacement of the submarine on the surface when

unloaded with fuel, ammunition, provisions, and crew.

2. Surface displacement Is the displacement of the submarine on the surface when

loaded with fuel, ammunition, provisions, and crew. It Is equal to the standard

displacement plus variable loads.

3. Submerged displacement is the displacement of the submarine when loaded,

operating submerged. It is equal to the surface displacement plus main ballast tanks.

The literature has many of the values of these displacements, but In many cases the

values differ slightly from one reference to the next. The literature usually provides no

more than two of the three displacements, but knowledge of two can yield a reasonable

estmate of the third. The variable loads and the ballast tank weight can be calculated

from these known displacements, or if known, can be used to calculate the

displacements.

Table 8-1 lists the displacement values for each of the submarines. Also shown are the

weights of the variable loads and main ballast tanks.

It should be noted that diesel electric submarines must have large-capacity auxiliary

ballast tanks to compensate for the lost weight of the bunker fuel. Alternatively, and

preferably, is the installation of a fuel compensating system, and using the fuel tanks as

SUBMARINE NAME

DISPLACEMENTS KILO WALRUS RUBIS BARBEL TYPE(Ltons) REF REF REF REF 2400 REF

STANDARD DISPLCMNT 1900 (e) 1900 (21) 2250 (e) 2146 (34) 1850 (17)VARIABLE LOADS 600 550 135 169 310

SURFACE DISPLCMNT 2500 (17) 2450 (21) 2385 (10) 2315 (34) 2160 (32)MN BALLAST TNKS 700 350 285 324 240

SUBMERGD DISPLCMNT 3200 (17) 2800 (21) 2670 (17) 2639 (34) 2400 (32)

FUNCTIONAL GROUP KILO WALRUS RUBIS BARBEL TYPEWEIGHTS 1700 REF 2000 2400

VARIABLE LOADS 600 550 135 169 (34) 310BALLAST TANK 700 350 285 324 (34) 240

Unless otherwise referenced, the following weights are from Appendix I.

MOBILITY MACHNRY 700 792 1073 575 ('34) 86BWEAPONS SYSTEMS 78 48 53 64 (34) 60C3I SYSTEMS 67 50 53 56 (34) 84SHIP SUPPORT 101 98 127 117 (34) 101STRUCTURAL WEIGHT 825 787 814 820 (34) 618FIXED BALLAST (5%) 128 125 129 514 (34) 119

SUBMERGD DISPLCMNT 3200 2800 2670 2639 2400

Table 8-1: Displacements and functional group weights.(Sheet one of two).

SUBMARINE NAME

DISPLACEMENTS TYPE TYPE SAURO VASTER- MIDGET(Ltons) 1700 REF 2000 REF REF GOTL'D REF 100 REF

STANDARD DXSPLCMNT 1760 (6) 1800 (6) 1280 (12) 990 (17) 100 (1)VARIABLE LOADS 380 264 200 80 24

SURFACE DISPLCMNT 2140 (5) 2064 (e) 1480 (12) 1070 (36) 124 (e)MN BALLAST TNKS 210 266 180 70 12

SUBMERGD DISPLCMNT 2350 (e) 2330 (6) 1660 (12) 1140 (6) 136 (1)

WEIGHTS TYPE TYPE SAURO VASTER- MIDGET(Ltons) 1700 2000 GOTL'D 100

VARIABLE LOADS 380 264 200 80 24

BALLAST TANK 210 266 180 70 12

Unless otherwise referenced, the following weights are from Appendix I.

MOBILITY MACHNRY 988 922 533 420 34WEAPONS SYSTEMS 42 59 71 76 16C31 SYSTEMS 32 40 61 41 6SHIP SUPPORT 67 76 70 49 aSTRUCTURAL WEIGHT 544 611 470 346 30FIXED BALLAST 86 93 75 55 6

SUBMERGD DISPLCMNT 2350 2330 1660 1140 136

Table 8-1: Displacements and functional group weights.(Sheet two of two).

-42.

auxiliary ballast tanks. This necessitates the installation of a reliable and effective fuel

oil filter and coalescer system as well. The literature was Inconclusive about the

presence of fuel-compensating systems, except for the TYPE 2400. which does.

Reference (32).

The ballast tank weight is a big selling point and Is also a matter of contention among

submarine builders and designers. In the event of hull damage severe enough to cause

flooding of the submarine, the bouyancy lost to the flooding water may be recovered, at

least temporarily, by blowing down the main ballast tanks, hence their alias as "reserve

bouyancy". Creating volume on a submarine Is expensive, and even the extra ballast

tank volume to accomodate a little extra reserve bouyancy will cost, in terms of speed,

range, payload, crew habitabilly, electronics, or construction cost. At the same time, It is

acknowledged that each manufacturer wishes to present his product In the best light

possible, and It is desirable to have large main ballast tanks, hence the source of the

tradeoff.

7.2 Functional Group Weights

The weights of specific machinery and other equipment aboard the submarines could

not be found in the literature. To estimate the functional group weights, empirical

formulas were developed which related data parameters which are found in the literature

to the elusive weight groups. Reference (16) was crucial in this regard. The details of

this process are described In Appendix I. The result of the Appendix I calculations for

functional group weights are listed in Table 8-1.

A rigorous analysis of the functional group weights given In Table 8-1 would be tongue-

in-cheek at best, since nearly all the weights are calculated from the same empirical

formulas. Instead, a qualitative approach will be taken In relating the weight groups of

.43-

each submarine to the other submarines, to attempt to understand how the overall

performance of each submarine is affected by the weights of its functional groups.

Using this approach, and with the aid of Figures 8-1 and 8-2, one may see that the boats

with the higher top speeds and longer endurance ranges, such as RUBIS, TYPE 1700,

and TYPE 2000, have the higher weights in the mobility functional area. Those with

lower top speeds, such as BARBEL, KILO, and MIDGET 100 have proportionately

smaller mobility weights.

The weights of the ship support, C31. and weapons functional groups are small

compared with the displacement of the corresponding submarine. This reflects the

nature of the materials from which these groups are constructed. It also reflects the

weight density of the spaces associated with those functional groups. It is reasonable to

expect that diesel engines, alternators, and lead-acid batteries make up a much larger

proportion of the displacement of the submarine than habitability or electronics spaces.

The vessels rated at a shallower Immersion depth, TYPE 2400 and MIDGET 100, have

a smaller proportion of their displacement attributed to structural weight. An exception is

BARBEL, rated at 120 meters immersion, whose structural weight is proportionatly as

great as submarines rated at 300 meters immersion. One reason for its higher structural

weight is that it, and KILO as well. is a double-hull design. One could conclude that the

empirical formulas of Appendix I are inaccurate by a factor of three, that the formulas

may be accurate but BARBEL is fabricated of a weaker material than the more modern

submarines, or that the formulas are accurate. but BARBEL is underrated at only 120

meters immersion.

-44-

bI-in

xx xlrr KA,

KX xx x i ]XI

M0XISi

lxx: xx xxx

0E

MWI yy e i r-yvi

4-0

ECi) xU x x x ~~i II V V

L xx-xx

A x.xo _X N PON X. X.- X. Ifl I

(n t- puin 94 0

Figure 8-1: Weights of submarine functional groups.

-2 $3ti

In-

CE t

4-

EE0M

C an

C -c

or

CC

44

- m 0 9- C in 0 iv N

Figure 8-2: Submarine weight allocation comparison.

-46.

Chapter 8

MILITARY PERFORMANCE

8.1 Propulsion and Mobility

The speed, range, and depth capabilities of a submarine are three of Its prime attributes,

and high values for each of these parameters is desirable, as they allow the submarine

to act with greater flexibility, and hence, greater effectiveness. Specific values of these

parameters are not available in the literature for the range of speeds of which these

submarines are capable. This section focuses upon developing such a comprehensive

database. Public-domain data germane to the mobility functional area is summarized in

Table 9-1.

8.1.1 Required Shaft Horsepower

The study commences with calculations of the maximum sustained speed of each

submarine. Extensive analysis of each submarine's propulsion characteristics are

performed In this study. Computer models of the hydrodynamic envelope are

established in Appendix B, and used to calculate the shaft horsepower required at

various speeds at deep and snorkel depths in Appendices C and D. The resulting values

of required shaft horsepower at deeply submerged depths are shown in Figure 9-1.

while the ratio of the larger shaft horsepower required when operating at snorkel depth is

depicted in Figure 9-2.

Figure 9-1 shows the characteristic cubic dependency of the power upon speed. for a

body moving in a viscous medium without the generation of gravity waves.

Figure 9-2 indicates humps and other irregularities in the speed/power curve for

operation at a depth where gravity waves are generated. The irregularities are caused

-47-

SUBMARINE NAME

PROPULSION KILO WALRUS PUBIS BARBEL TYPEAND MOBILITY REF REF REF REF 240() REF

SUBMRGD SPD, Ref 25 (17) ". 25 (.17') 21 (17) 20 '32SUBMRGD SPD, Calc 18 20 25.1 17.8 20.5SURFACE SPEED 12 :17: 12 (7) 20 (17) 15 (17) 12A' (32)SNORT SPEED 10 (e) 12 (7) N/A I) (e) 10 (32)

SHP INSTALLED, HP 4000 (17) 5360 (7) 10000 (e) 3150 (17) 5400 (17)ALTERNATOR CAP, KW 4480 (e) 5170 370 (e) 358 2500 (32)DIESEL CAP, HP 6000 (e) 6930 (11) 500 (e) 480 (17) 3618 (32HOTEL LOAD, Kw 124.5 124.7 129.7 94.38 115.9BUNKER FUEL, Lton 270 (e) 275 (e) 19.4 130 (e) 186.7 (32)

IMMERSION, Meters 300 e) 3,') (24) 300 (.()) 120 (e) 200 5:)

NP OF MAIN MOTORS: 2 e. 1 (5) 1 (17) 2 17) 1 (5)EMERGENCY MOTOR? YES (.e) YES Ce) YES (8) YES (e) YES (e)FWD PLANE POSIT SAIL (e) SAIL (:24:) SAIL (8) SAIL (35) HULL (13)STERN PLANE FORM C:ROSS e) x" (24) :ROSS (8) CROSS (35) CROSS (13)BOW THRUSTERT. NO e) NO (24) NO (e) NO (35:) NO (13)

NUMBER OF CELLS 480 (e) 480 (7) 121) (e) 504 (35) 460 (32)WEIGHT, Ltcn 275 (e) 275 68.75 (e) 290 275 (32)2

VOLUME, cu ft 4000 (e) 4007 1000 (e 5700 4675HIGH-END VOLTAGE 590 (e) 590 (e) 276 (e) 580 (e) 590 (32)LOW-END VOLTAGE 440 C ..e) 440 (e) 228 (e) 479 (e) 440 ( 32)

BATTERY ENERGY KW-Hrs KW-Hr s KW-Hr s KW-Hrs KW-Hr s@ 100 Hr Rate 11280 1128(0 2620 11844 11280')

Table 9-1: Propulsio, n plant and cther mobility gro, up parameters.(Sheet one of two.).

-48-

SUBMARINE NAME

PROPULSION TYPE TYPE SAURO VASTER- MIDGETAND MOBILITY 1700 REF 2000 REF REF GOTL'D REF 100 REF

SUBMRGD SPD, Ref 25 (7) 25 (6) 19.3 (12) ? 18 (33)SUBMRGD SPD, Calc 24.7 25 19.3 20 16.8SURFACE SPEED 13 (7) 13 (6) 11 (12) 11 (17) 8 (e)SNORT SPEED 15 (7) 15 (6) 11 (12) 10 (e) N/A (33)

SHP INSTALLED, HP 8844 (7) 7500 (6) 4207 (12) 2537 420 (29)ALTERNATOR CAP, KW 4400 (7) 3600 (6) 2160 (12) 2000 90DIESEL CAP, HP 6000 5400 (6) 2894 (12) 2680 (19) 120 (29)HOTEL LOAD, Kw 114.9 108.2 88.13 63.88 15 (1)BUNKER FUEL, Lton 319 (7) 236 (6) 144 (12) 40 7.668

IMMERSION, Meters 300 (:7) 325 (5) 300 (12) 300 (e) 200 (29)NR OF MAIN MOTORS: 1 (7) 1 (e) 1 (12) 1 (e) 1 (29)EMERGENCY MOTOR? YES (e) YES (e) YES (e) YES (e) 48HP (29)FWD PLANE POSIT SAIL (2) HULL (e) SAIL (12") SAIL ('36) SAIL (33)STERN PLANE FORM CROSS (2) CROSS (e) CROSS (12) X" (36) CROSS (33)BOW THRUSTER? NO (2) NO (e) NO (12) NO (36) YES (33)

BATTERY CELLS 960 (e) 720 (5) 296 (5) 168 (7) 13 (e)BATTRY WGT, Lton 550 412.5 170 96.25 8.6BATTRY VOL, cu ft 9989 7013 2371 1509 90BATTRY VOLT (HIGH) 590 (e) 590 (e) 680.8 (e) 420 (19) 29.9BATTRY VOLT (LOW) 440 (e) 440 (e) 562.4 (e) 285 (19) 24.7

BATTERY ENERGY KW-Hrs KW-Hrs KW-Hrs KW-Hrs KW-Hrs* 100 Hr Rate 22560 16920 6956 3948 305.5

Table 9-1: Propulsion plant and other mobility group parameters.(Sheet two cf two).

-49-

Shaft Horsepower RequiredAm au A tb n if Spud

10 -

//

4--

I--

2 0 10 14 is 22 20

SPEED, onILO 4- VLdmU I . ll. x ME 2400

Shaft Horsepower Required

1 * -a a unibn of Spemd

1 1

/

i!SPED ,,.( -,'

Fi.r 9-1 Re u rd S at H r e o e t v r o s s ed . (h e f 2

. . -- -. ..-- - - - - - - - - - - - - - - - - - - -

I- -.-- - . - ---

4.0,* I1 1 -. l

SP[DIK

I~~f'PE OOO . *. -aUI ' , .IO'anD:: I-

1 - - --e -I: Rqie Shf-oreoe -tvriu - -es See f2

-6-J

.. .... i. 0-mim, ,*~lll lllill l - -i i-

-50-

Shaft Horsepower Required460* - Am orubn mf Uomi_____

330-

30

100

ILO 4- VAmuS R4 ll A MABEL x Wfi 20

Shaft Horsepower Required40- _____An. a unctn uf Spiud__________

360-

3

SPEED, oft+ 1y~t 2000 4 SAUPO, %UENOTA ~S!G~ b

Figure 9-1: Required Shaft Horsepower at various speeds. (Sheet 2 of 2)

Ratio of SHP Required at Speed

1.3 - - - - - - - - - - - - -

I o

a 4 0 10 12 14

a KILO 4 L#US I SOBEL x MEW 2400

Ratio of SHP RequiredOSncrbllno buoflh)'tmpuy lub mwm sO

. 1.2

0.8

PC 10 M- YYWP 2000 WOO' 4L

Figure 9-2: Ratio of SHP required at Snorkel Depth to SHiP required-at Deep Sublergetice Depth.

.52-as the generated waveform alternately hinders to a greater extent, then to a lesser

extent, then to a still greater extent, the progress of the submarine through the water.

This wave drag may be predicted as a function of Froude Number, and submergence

ratio, according to the method of Appendix D.

8.1.2 Fuel Endurance Range

The endurance range based upon bunker fuel load Is calculated In Appendix E. and the

results are displayed In Figure 9-3.

This Is In general quite a lengthy range, since the submarines are loaded with enough

fuel to travel goodly distances at higher speeds, and the speed for maximum fuel

endurance Is usually In the vicinity of four or five knots. The fuel endurance range Is not

the final word on endurance range for the submarine, considering all factors, but It Is an

excellent way to compare designs In the area of hull efficiency and amount of bunker

fuel loaded. The fuel endurance range Is calculated conservatively, using the value of

SHP at snorkel depth, since much of the transit would be accomplished under this

operating condition.

There Is an economy of scale concerning range. Since the SHP required Is a function of

the wetted surface area of the submarine, and since the amount of diesel fuel (or the

number of battery cells, or the number of days of provisions), which can be carried Is a

function of the Internal volume of the submarine, then the endurance range of a

submarine will Increase for Increasing displacement, all else being equal.

To compensate for its low endurance range, the MIDGET 100 Is equipped with a bow-

mounted towing cable, which would allow It to be deployed from a mothership when

within a manageable range of the operating area.

Appendix E gives a relation for calculating the optimum speed for maximizing fuel

endurance range.

-51-Snorkelinq,.iFuei Endumnce Founqe

1rr -

12 -- 1 --

1-

1.5-

, ; , , +. " - ,E E- , ; _ * a. .

,",,,. ..., _ , . - -. - -

+ *4

-1 - -lP . -. -4 -: -

.Sn d~eing"F El nduralnce Ralnge12 -

-4 . i -"f,. -

0 *1.4.,.,

FigurerI 9-3:)F~e Endurac ag ae p n e losnoreldeth

11 - " --- - f- " .

1 4 - v '- - ":.. --.. -.... -"1 - - . -, ..,-

i8 - - ::. -" - - - - --. 4-" -

2l - -.. ------ - --

,i 4 f lI ""'

2410 12 4.+

Figure 9-3: Endurance range based upon fuel load, at snorkel depth.

-S4-

8.1.3 Battery Endurance Range

The battery endurance range Is calculated In much the same way that the fuel

endurance range Is calculated, except that the source of power Is the storage battery

Instead of diesel fuel. Battery endurance range Is of great Importance nilltadly, since

the submarine may travel much more quietly on electric motor than on snorkeling diesel,

and Is also much less susceptible to radar and Infrared detection than when snorkeing.

The problem with calculating battery endurance range Is that the available energy to

propel the submarine decreases as the rate of demand for It (the power level) Is

Increased. This Is due to the fact that at high power rates, as much as forty-percent of

the stored chemical energy Is dissipated as heat, and Is unavailable for useful work.

Further discussion of this Is contained In Appendix F.

The calculation of the battery endurance range Is conducted In Appendix G, and the

resulting plot Is shown In Figure 9-4. An Inspection of Figure 9-4 reveals the advantage

of outfitting a submarine with a large battery, when submerged endurance counts. The

tremendous battery range of the TYPE 1700 is due primarily to Its very large battery, and

also to its moderate hotel load and required shaft horsepower.

RUBIS has a low battery endurance range because It Is equipped with a small battery.

MIDGET 100 has a very small battery, and a relatively high hotel load as well. Both of

these subs have primary propulsive power which Is Independent, to a degree, of the

atmosphere, and so the need to avoid snorkeflng Is not present. RUBIS and MIDGET

100 presumably have a battery just large enough allow them to operate stealthily for a

short mission, perhaps just enough power to operate hotel services while remaining as a

silent sentry or picket at bare steerageway.

The RUBIS has a nuclear reactor to generate steam for the turbo-alternators. which

produce electric power for the main propulsion motor and hotel electricity.

-55-

B ctter',' Endurance R:anqe

ande -

son -_________

200 -

P

-6~Z-

100 - ________

________

0- _____--_,..____

o *1 + 6 : 1. old

Bttery Endura nce Raonge

C'OO - __ _ -+__ --_ __--_-_

*r -... .

.

400 -

3 . -,In ...0 -

r-" . + 4WO

Figure 9-4: Endurance range based upon battery capa

city. (Sheet I of 2)

80% D oD.

-56-

Battery Endurance Rangeaha a rundbn of Sped

lab -- - - - - - - - - - - - - - - -

174 -- - - - - - - - - - - - - - - -110 -1SO --

1a -- - - - - - - - - - - - - - - -

140

130

110 --------------------------------

130 -- - - - - - - - - - - - - - - -

----------------------------------

* ' m -------- ------0

30----20 -

11 21 23 25

101 + -2 "

Battery Endurance Rangeao --

150 -- - - - - - - - ---

00 ---- " -6- - ",. - .,.a.- -

170 -140 "---- -.-

30b-- - --- - - --110 - - - - ""

1 0 0 - .. ..

4 O 66

Fu9 - E a n bae upon ace280%- .o, _120

11 13 is 17 101 21 ,23 23

WEDpr, Pft

Figure 9-4: Endurance range based upon battery capacity. (Sheet 2 of 2)

80% DoD.

.57.

The MIDGET 100 has a closed-cycle diesel main propulsion engine clutched to the main

shaft. There are also two smaller closed-cycle diesel alternator sets, which supply hotel

electic, charge the battery, and can supply the emergency electric propulsion motor.

8.1.4 Indiscretion Rate and Interval

Indiscretion rate, evaluated at a particular speed, Is the fraction of time which a

submarine must spend snorkeling, In order to charge Its battery. Indiscretion Interval,

evaluated at a particular speed, Is the duration of time which elapses between

Indiscretion periods.

The Indiscretion rates of each of the submarines Is calculated in Appendix H, and is

displayed for the range of snorkel-capable speeds In Figure 9-5. As expected, the

submarines with large batteries and large alternator capacities have the lowest

Indiscretion rates for a given speed. As discussed In Appendix H, the alternator capacity

is very Important In keeping Indiscretion rate low, because the recharging time is less.

However, there Is a limit to the recharging rate, since the same type of Inefficiency exists

In recharging the battery as in drawing power from it.

The Indiscretion Interval Is also discussed and computed in Appendix H, and the results

are shown In Figure 9-6. For very low speeds, the Indiscretion Interval becomes much

greater, then tapers off to a maximum. The batteries of all of the submarines benefit

from being operated at a lower power level, which frees up more available energy, and

accentuates the already increasing Indiscretion Interval.

8.1.5 Overall Endurance Range

For the purposes of this study, overall endurance range shall be defined as the range

the submarine can achieve at constant speed, all factors considered. In other words,

when the submarine exhausts one set of supplies, be it fuel, water, provisions, or

-58-Indiscretion Rote

0.!

/

a +/

-ls --.-

i "

0.00 - -- -"- .-

24 0 t0 10 12 14

£pPr!b, leua a1 + 1 tA N

KILO WALRUS BARBEL TYPE 2400

Indiscretion s 80 te

" 4'V

9.' */

0.0-------------------

24 0 6l 10 1 14

Figure 9-5: Indiscretion rate at snorkeling speeds, 80Y4 D~oD.

-39-

Indiscretion Interval Lit 80% DoD

1ISO -

14a- -

130 -

120110 ----

100-lid -

I 0 . -- -.

40--

30

20

2 10 14 1 22 28

Spend, Ioo 1 + 02 CLN

Indiscretion Interval at 8,7.e% DoD

1IS- -

ISO

120 a

11-

In:

'Il

o - ---'a--% .,

40 -d

30- - __

20 --- 4 - .- ------------ -

10-0 - - . :j h /In 1 14 1S 22 28

Speed, MeuO 8+ WT f.:

Figure 9-6: Indiscretion interval at snorkeling speeds, 80% DoD.

battery, It has completed Its Journey, and Its range at that speed Is defined as the length

of that Journey. However, battery range does not figure Into overall range, since the

battery may be recharged as long as there is fuel remaining. So overall range will

depend upon whether provisions or fuel are exhausted first at a given speed.

Figure 9-7 shows plots of provision and fuel range for speeds between two and ten

knots. Provision range Is directly proportional to the vessel speed, since the time rate of

provision consumption Is assumed constant. If a submarine were to be designed solely

to maximize endurance range at a constant speed, then Ideally provisions and fuel

would be exhausted simultaneously, at the speed of best fuel endurance range. Real

diesel-electric submarines usually need extra fuel since they may need to conduct high-

speed actions which require more fuel per mile. As such, Figure 9-7 reveals that nealy

all of the conventionally-powered boats have provision ranges less then their fuel range

at the optimum fuel range speed. This Indicates a deliberate loading of additional fuel to

allow the overall range to be Increased, and for It to occur at a greater speed.

For the nuclear-powered RUBIS, the overall range Is normally taken as the provision

range. The fuel range on emergency diesel, with 100% expenditure of bunker fuel, Is

shown In Figure 9-7 for comparison.

8.2 Weapons Systems

8.2.1 Weapons Launching Systems

The number, length, diameter, and launching method of a submarine's torpedo tubes are

Important military parameters. They determine the size and type of weapon which may

be employed by the submarine. The number of torpedo tubes is related to the number

of weapons which may be fired in a salvo, and perhaps also to the fire rate. Whether a

submarine has the ability to track multiple targets and direct multiple weapons to those

targets was not available In the open literature.

-61- -

Provision vs Fuel Endurance: KILO

18

13 8

11 _

14

1-A

24

11_

/ __ ,.... _-'

a.-

3..

1~

24 8 B 10

Speed, 9% "

0 Pdn nod + Snau:a-I Pang@

7igure 9-7; Provision Endurance plotted with Fuel Endurance. (Sheet 1 of 5)

-62-

Provision vs Emergency Fuel: RUBIS

13712-____

11

13

PraASnoodg, ou0 pa~w M+ Cmnuukw Range

Fiur 97:Provision vuacs lotwt Fuel Endurance (Shet2EoL5

-63-Provision vs Fuel Endurance: TYPE 2400

12

10 _____

A r

2 4 a 1

loved, IS.a pmu%4da nu + snack-01 Range

Provision vs Fuel Endurance: TYPE 1 700

1-

0-

S mund, IS.O Pon-Aslarn + Sna*.I Pangs

Figure 9-7: Provision Endurance plotted with Fuel Endurance. (Sheet 3 of 5)

-64-

Provision vs Fuel Endurance: TYPE 2000I?

20 4 S

Spend. EnO3 IInAWd m + snorkel Range

Provision vs Fuel Endurance: SAURO

10

14 -

13 - ____

12 -

11 -_____ __________

24 10 i

Spend, IMuo Pro-4Amlon + Snorkel Rannge


-65-Provision vs Fuel Endurance: VASTERG'ND

13.

14.

11'12

11-

1- .______ '

4-

3. -

3.4 - _ _ _ _ _ _ _ _ _

3.2

1. -

2.2 ..

1.4 ____"

1.2. -.

1.1 f0.8

2 48 10

O3 PftA4WO m + Snoii:el Ponge


The launching system Is Important because It determines whether cruise missiles may

be fired from the torpedo tubes. At this time, nothing was found In the open lterature to

state that swim-out encapsulated cruise missiles have been developed, so any

submarine not using some type of positive ejection system to launch weapons cannot

employ cruise missiles. It Is the author's opinion however, that self-launching cruise

missiles may be In development.

The standard tube diameter In the West Is 21 Inches (533mm) which will accomodate

the heavyweight torpedoes and encapsulated cruise missiles made In the West.

Lightweight torpedoes are 15 Inches In diameter, and are carried on surface ships,

aircraft and some smaller submarines, such as the MIDGET 100.

Table 9-2 fists weapons systems parameters. The term "Water Slug" Is used to denote

a positive ejection launch mechanism, although the details of the exact type were not

found In the literature. Note that KILO, WALRUS, RUBIS, BARBEL, and TYPE 2400

employ positive ejection methods while the remaining five do not.

Evaluating the combat systems effectiveness of a submarine based upon the number of

tubes and reload torpedoes possessed Is tricky. On one hand, the assumption could be

made that all torpedo tubes have equal fire and reload rates, and that each submarine

can compute and maintain fire control solutions for as many targets and torpedoes as it

Is equipped with torpedo tubes. In this scenario, advantage clearly belongs to the

submarine with the most tubes. On the other hand, It could be assumed that a designer

equips a given submarine with an abundance of tubes because of anticipated poor tube

reliability, or poor weapon kill probability. In actuality, there is not enough data in the

open literature to make a detailed evaluation of the combat systems effectiveness. For

the purposes of this study, It shall be assumed that all torpedo tubes have equal fire and

reload rates, and that each submarine can compute and maintain fire control solutions

for half as many targets and torpedoes as it is equipped with torpedo tubes.

-67-

SUBMARINE NAME

WEAPONS SYSTEMS KILO WALRUS RUBIS BARBEL TYPEPARAMETER REF REF REF REF 2400 REF

PRIMARY TORP TUBES 8 (17) 4 (7) 4 (10) 6 (35) 6 (32)OTHER TUBES 0 (17) 0 (7) 0 (10) 0 (35) 0 (32)

NUMBER OF RELOADS 10 (17) 20 (17) 10 (10) 6 (35) 12 (32)TUBE DIAM, (in) 21 (e) 21 (7) 21 (17) 21 (35) 21 (32)

TORPEDO LAUNCH WATER (e) WATER (16) WAIE, (e) WATER (e) WATER (32)METHOD SLUG SLUG SLUG SLUG SLUG

TORPEDO NAME MK-48 (22) F17P (22) MK-48 (22) SPEARFISHTORPEDO SPEED, Kts 50 (e) 55 (22) 40 (e) 55 (22) 70 (22)WARHEAD WGT, Kg 300 (e) 300 (22) 250 (22) 300 (22) 180 (e)TORPEDO RANGE, Km 40 (e) 45 (22) 40 (e) 45 (22) 45 (22)

CRUISE MISSILES? YES (e) YES (17) YES (22) YES (e) YES (22)MAX NMBR CARRIED 18 (e) 24 (17) 14 (17) 12 (e) 18 (e)MISSILE NAME SSN-21(26) UGM-84(17) SM-39 (22) UGM-84 (e) UGM-84(22)MISSL RANGE, Km 125 (e) 125 (e) 50 (17) 125 (e) 125 (e)WARHEAD WGT, Kg 150 (e) 150 (e) 125 (17) 150 (e) 150 (e)

MINE-LAYING? YES (23) YES (e) YES (e) YES (e) YES (32)MAX NMBR CARRIED 20 (e) 40 (e) 20 (e) 12 (e) 24 (e)WHERE CARRIED WITHIN (e) WITHIN (e) WITHIN (e) WITHIN (e) WITHIN(32)DEPLOYMENT METHOD TUBES (e) TUBES (e) TUBES (e) SELF (e) TUBES (32)WARHEAD WGT, Kg 600 (e) 600 (e) 600 (e) 300 (e) 600 (e)

SWIMMERS CARRIED? YES (e) NO (e) NO (e) NO (e) YES (32)AIRLOCK CAPACITY 3 (e) N/A (e) N/A (e) N/A (e) 5 (32)SWIMMER CHARIOTS? NO (e) NO (e) NO (e) NO (e) NO (e)MAX NMBR POSSIBLE N/A (e) N/A (e) N/A (e) N/A (e) N/A (e)

AAW ROCKETS MAYBE (17) NO (e) NO (e) NO (e) NO (e)NUMBER ? (17) N/A (e) N/A (e) N/A (e) N/A (e)GUNS NO (e) NO (e) NO (e) NO (e) NO (e)CALIBER N/A (e) N/A (e) N/A (e) N/A (e) N/A (e)

Table 9-2: Weapons Systems parameters. (Sheet one of two).

-68-

SUBMARINE NAME

WEAPONS SYSTEMS TYPE TYPE SAURO VASTER- MIDGETPARAMETER 1700 REF 2000 REF REF GOTL'D REF 100 REF

PRIMARY TORP TUBES 6 (7) 8 (5) 6 (5) 6 (36) 4 (1)OTHER TUBES 0 (7) 0 (5) 0 (5) 3 (36) 0 (1)

NUMBER OF RELOADS 16 (7) 12 (5) 6 (5) 6 (36) 0 (29)TUBE DIAM, (in) 21+ (7) 21+ (e) 21 (5) 21B,15(36) 15+ (33)

TORPEDO LAUNCH SWIM (7) SWIM (5) SWIM (12) SWIM (36) SWIM (1)METHOD OUT OUT OUT OUT OUT

TORPEDO NAME SEAL (22) SEAL (22) A184 (22) TP617 (22) (LWT) (33)TORPEDO SPEED, Kts 35+ (22) 35+ (22) 50 (e) 60 (22) 40 (e)WARHEAD WGT, Kg 260 (22) 260 (22) 250 (e) 250 (22) 50 (1)TORPEDO RANGE, Km 35+ (22) 35+ (22) 28 (22) 70 (e) 12 (e)

CRUISE MISSILES? NO (e) NO (e) NO (e) NO (e) NO (e)MAX NMBR CARRIED N/A (e) N/A (e) N/A (e) N/A (e) N/A (e)MISSILE NAME N/A (e) N/A (e) N/A (e) N/A (e) N/A (e)MISSL RANGE, Km N/A (e) N/A (e) N/A (e) N/A (e) N/A (e)WARHEAD WGT, Kg N/A (e) N/A (e) N/A (e) N/A (e) N/A (e)

MINE-LAYING? YES (e) YES (e) YES (e) YES (36) YES (29)MAX NMBR CARRIED 32 (e) 24 (e) 12 (e) 22 (e) 10 (29)WHERE CARRIED WITHIN (e) WITHIN (e) WITHIN (e) PODS (7) PODS (29)DEPLOYMENT METHOD SELF (e) SELF (e) SELF (e) SELF (7) PLACED(29)WARHEAD WGT, Kg 300 (e) 300 (e) 300 (e) 600 (e) 600 (29)

SWIMMERS CARRIED? YES (31) YES (31) NO (e) NO (e) NO* (29)AIRLOCK CAPACITY 3 (e) 3 (e) N/A (e) N/A (e) N/A (29)SWIMMER CHARIOTS? NO (e) NO (e) NO (e) NO (e) NO* (29)MAX NMBR POSSIBLE N/A (e) N/A (e) N/A (e) N/A (e) N/A (29)

AAW ROCKETS YES (31) NO (e) NO (e) NO (e) NO (e)NUMBER 4 (31) N/A (e) N/A (e) N/A (e) N/A (e)GUNS NO (e) NO (e) NO (e) NO (e) YES (1)CALIBER N/A (e) N/A (e) N/A (e) N/A (e) 40mm&2Omm

Table 9-2: Weapons Systems parameters. (Sheet two of two).

.69-

8.2.2 Torpedoes

Torpedoes have been the weapon of choice for submarine use. Although much slower

than guns or missiles, the torpedo Is employed very effectively by submarines because

of the submarine's stealth. Because the torpedo warhead explodes beneath the surface

of the water, it Is more damaging to the hull structure of a surface vessel than an

equally-sized missile warhead.

There are several heavyweight torpedoes manufactured In the West, all of which are

compatible with the free-world submarines of this study. All are effective weapons within

their firing envelopes. The size of the envelope Is the Important criteria. and Is governed

by the speed, range, and depth capabilities, by the onboard sensing and logic systems,

and by the presence or absence of a datalink to the parent submarine. Superior speed

is needed to overtake the target, the rule of thumb being twice the anticipated target

speed, Reference (14). Sufficient range and depth capabilities are also necessary to

complete the pursuit, and the sonar and logic circuits aboard the torpedo are Important

for terminal guidance. The datalink (such as wire-guidance) with the mother sub is

Important for mid-course guidance.

Perhaps the most capable heavyweight torpedo In the West Is the MK-48 ADCAP.

Reference (14), primarily because of its speed, range, and depth capability, the exact

values of which are classified. However, the torpedo parameters listed in Table 9-2 are

suitable for comparison.

8.2.3 Cruise Missiles

The capability of a submarine to carry cruise missiles gives the it the medium-range (50

nautical mile) stand-off attack mode against surface targets which was previously the

province of only surface ships and attack aircraft. Only those submarines equipped with

-70.

a positive ejection system (and the requisite fire control electronics) may currently

employ cruise missiles. Fire control solutions would most likely be gained by passive

array sonar, which may have ranges up to 45 kilometers or more, the exact values being

classified.

The ability of a submarine to carry cruise missiles Is clearly an advantage. For those

ships able to employ them, encapsulated cruise missiles may be loaded in lieu of

heavyweight torpedoes on a one-for-one basis.

8.2.4 Mine Laying

A submarine, particularly a diesel-electric submarine, Is Ideally equipped because of Its

stealth to conduct covert mining operations. Many offensive mining scenarios call for

covert placement of the mines. In general, two small mines may be loaded In lieu of one

heavyweight torpedo. Table 9-2 lists mine laying parameters. Submarines not equipped

with positive ejection tubes must employ self-propelled mines. Kockums Shipyard,

manufacturer of the VASTERGOTLAND, has developed an external mine-belt

conveyance system, the advantage of which Is that a full load of mines may be carried

without affecting the torpedo load.

8.2.5 Other Weapons Systems

The use of combat swimmers for reconnalsance and other activities Is believed to be a

primary mission area of some diesel-electric submarines. It Is known that the TYPE

2400, TYPE 1700, and TYPE 2000 submarines are equipped with swimmer lockout

chambers, detailed in Table 9-2. KILO is judged by the author to have this capability as

well. A variant of the MIDGET 100 is constructed with a four-person swimmer lockout

chamber instead of the four lightweight torpedo tubes. The MIDGET 100 may also tow

swimmer delivery vehicles to the operating area, but this must reduce its endurance

range.

-71.

KILO may be equipped with anti-air missiles mounted in the fairwater. These may have

been installed In response to the high state of aircraft-based anti-submadne warfare

(ASW) capabilities among NATO forces.

MIDGET 100 Is equipped with a 20mm and a 40 mm deck gun. This further Indicates

that the primary mission area of this vessel is special operations.

8.3 Command, Control, Communication, and Information

8.3.1 Sonar

The primary sensor of the modern submarine Is passive sonar. The structure of the

sonar may be conformal hull-mounted array, trailed linear array, or spherical, cylindrical

bow-mounted array, or a composite sensing system made up of several of these arrays.

The advantage of passive sonar is that the submarine can remain undetected while

observing Its environment. A submarine with a passive sonar Is able to determine the

bearing of a sound source. When equipped with a sensitive conformal or trailed linear

array, the submarine can get range information as well from the time delay in reception

of the incident sound waves. With range and bearing information, the computation of fire

control solutions is possible.

Active sonar is usually used tactically to confirm the computed target range by a single

active "ping" immediatly prior to weapon launch. It is typically at this point that opposing

sonar-equipped vessels, both surface ships and other submarines, first become aware

of the sub's presence. For reasons of stealth, active sonar is not often used by a

submarine on patrol.

The quintessential parameter of sonar performance is sensitivity. Sensitivity and

discrimination, to be able to detect a potential target and separate its sound from the

ambietit noise in order to verity its existence and possibly its identity. The detection

-72.range Is dependent upon the sensitivity of the sonar, and detectability Is the "name of

the game" when stealth and first-strike capability are of paramount Importance.

Unfortunately, because of Its Importance, detection capabilities of sonar equipment is not

available In the literature. The literature does have Information on the manufacturers.

and in some cases the particular model, of the various sonars installed in the subject

submarines, as may be seen in Table 9-3. All of the submarines in this study are

equipped with both active and passive sonar, and most have a towed linear or flank

conformal array sonar as well.

8.3.2 Periscopes

The traditional submarine sensor is the periscope. Modem periscopes are equipped

with telescopes, rangefinders, infrared adapters, and electro-optical and photographic

adapters. All of the submarines in this study are equipped with two periscopes. search

and attack. It is the author's opinion that every submarine Is fitted with the above

mentioned periscope augmentation gear, although the literature did not confirm this.

The names of the periscope manufacturers are listed with their host submarines in Table

9-3.

8.3.3 Radar

Radar Is used by submarines primarily for navigation during sea detail and other

navigational situations, but could also be used in a combat role. Of particular interest is

the Decca radar mounted on WALRUS. The Decca is popular on a number of

commercial vessels, so the employment of it by WALRUS in a crowded shippino lanp

(and under limited visibility conditions) would not raise alarm. Available radar

information is listed in Table 9-3.

SUBMARINE NAME

COMMAND KILO WALRUS RUBIS BARBEL TYPE

AND CONTROL REF REF REF REF 2400 REF-------------------- -------- ----------------------------------

SHIPS SENSORSPASSIVE SONAR YES (17) SIASS (22) DSUV22(17) YES (35) T-2019 (7)ACTIVE SONAR YES (17) OCTOPUS DUUA2B(17) BQS-4 (17) T-2040 (7)ARRAY SONAR YES (e) T-2026 (7) DUUX-5(17) ? TOWED (7)RADAR SNOOP (17) DECCA CALYPSO YES (35) T 1007 (7)ELECT SURVEILLNCE YES (e) SIGNAAL YES (e) YES (35) RACAL (7)PERISCOPES YES (e) KOLLMORGAN SOPELEM 2 (35) BARR&STROUXBT NO (e) NO (e) NO (e) YES (e) YES (32)INERTIAL GUIDANCE SEMI (e) NO (e) NO (e) SEMI (e) SEMI (e).................................J.......... .......... . .............

COMMMUNICATION SYSTEMSU/W TELEPHONE ? YES (e) TUUM WQC-2 YES (32)HF RADIO YES (e) YES (e) YES (e) YES (e) YES (32)VHF RADIO YES (e) YES (e) YES (e) YES (e) YES (32)UHF RADIO YES (e) NO (e) YES (e) YES (e) YES (32)VLF RADIO YES (e) NO (e) YES (e) YES (e) (LF) (32)..... ... ....... l....e..e......................................

AUTOMATED CONTROL STATIONSSHIP CONTROL ONE-MA(12)

MFGR: SOME (e) SEWACO(1S) YES (e) SOME (e)MODEL: VIII (18)

FIRE CONTROL YES (32)MFGR: YES (e) THOMSON- ? FERRANTI-

SIGNAAL SINTRA GRESHAMMODEL: GIPSY (7) MK-101 DCC

PROPULSIONMFGR: SOME (e) YES (e) YES (e) SOME (e) YES (32)MODEL:

Table 9-3: Command, Control, Communication, and Information systems.(Sheet one of two).

- " r • i a I i - I I I .... . .

SUBMARINE NAME

COMMAND TYPE TYPE SAURO VASTER- MIDGETAND CONTROL 1700 REF 2000 REF REF GOTL'D REF 100 REF

SHIPS SENSORSPASSIVE SONAR KAE (7) CSU 3-4 IPD 70/S KAE CSU-83 YES (7)ACTIVE SONAR KAE (7) CSU 3-4 IPD 70/S KAE CSU-83 YES (7)ARRAY SONAR DUUX-5 (7) CSU 3-4 IPD 70/S YES (36) NO (e)RADAR SMA (7) YES SMA 3RM20 THERMA(36) NO (e)ELECT SURVEILLNCE NO (7) YES YES (12) ARGO (7) NO (e)PERISCOPES KOLLMORGAN 2 KOLLMORGAN BARR&STROUD (TWO)(33)XBT YES (e) YES (e) NO (e) NO (e) NO (e)INERTIAL GUIDANCE NO (e) NO (e) NO (e) SEMI (36) SEMI (e)

COMMMUNICATION SYSTEMSUNDERWATER TELEPHONE YES (e) YES (12) YES (e) NO (e)HF RADIO YES (e) YES (12) YES (36) YES (e)VHF RADIO YES (e) NO (12) NO (e) YES (e)UHF RADIO YES (e) YES (12) YES (36) NO (e)VLF RADIO NO (e) YES (12) NO (e) NO (e)

AUTOMATED CONTROL STATIONSSHIP CONTROL

MFGR: SAGEM (31) YES (e) YES (12) SAAB (19) YES (29)MODEL:

FIRE CONTROLMFGR: SIGNAAL YES (e) SEPA DATA (36) YES (29)

SAABMODEL: SINBADS MK-3 NEDPS (36)

PROPULSIONMFGR: YES (7) YES (e) YES (e) YES (e) YES (29)MODEL:

Table 9-3: Command, Control, Communication, and Information systems.(Sheet two of two).

.75-

8.3.4 Electronic Surveillance Measures

Electronic surveillance (ESM) is a more valuable combat tool than radar because the

submarine does not reveal itself when using ESM. ESM is the passive sonar of the

electronic Information realm, and may be used to assist in the Identification of a contact.

The manufacturers of the submarine ESM gear are listed In Table 9-3.

8.3.5 External Communications

Table 9-3 lists the available information on communications systems.

The necessity of a submarine to be able to communicate with friendly operating forces is

essential. Because of data links with aircraft and other surface units, surface ships

generally have knowledge of a much greater area than submarines. The submarine

must communicate with friendly forces in order to cooperate most effectively with friendly

forces. The methods of communication available are various radio frequency bands,

and underwater telephone. High frequency (HF) radio is generally used to communicate

with shore stations by teletypewriter. Very high frequency (VHF) radio is used to

communicate at distances just beyond the horizon. Ultra high frequency (UHF) is useful

for line-of-sight communication, and as such has a shorter range but will allow the

submarine to remain undetected to surface units beyond the horizon. Very low

frequency (VLF) radio receivers were designed for use aboard strategic ballistic-missile

submarines, but have been installed on some patrol submarines as well.

Underwater telephone may be used for two-way communication while the submarine is

submerged, which is not possible with radio. Underwater telephone uses encoded

sound pulses sent through the main active sonar array or through a separate dedicated

transducer. It has limited range.

-76-

8.3.6 Automated Controls

Automated control systems have revolutionized the design of the submarine. By

automating the propulsion and auxiliary plants, and Integrating and computerizing the

sensors and command centers, the required complement has been halved. A smaller

complement frees up space and weight for other areas such as provisions. fuel. battery.

or weapons reloads. The volume and weight cost of automating Is less than the volume

and weight saved due to the crew reduction It allows. The other costs of automating are

a sharp Increase In system complexity, with a multiplication of the probability of system

failure, a decrease in systems availability, and an Increase in preventative and corrective

maintalnance actions. Additionally, during casualty situations, when manual backup

may become necessary, It Is an advantage to have a high man-to-equipment ratio.

All of the submarines except BARBEL and possibly KILO use advanced automation

technology and hardware. TYPE 1700, TYPE 2000, VASTERGOTLAND, and MIDGET

100 use it the most extensively, and with good results. Manufacturers of automation and

control hardware are listed in Table 9-3.

8.4 Ship Support

The ship support functional group is concerned with the amount of space and weight

needed to support the mobility, weapons, and C31 groups. It is made up of the

habitability spaces, passageways, and provisions, and Is directly proportional to the

number of crewmembers. Depending upon one's viewpoint, the crew may or may not be

Included in the ship support functional group, but for this study. the crew itself is

considered to be an integral and operational part of the other three functional groups.

So ship support systems do not contribute directly to the performance of the submarine's

mission, but are nonetheless essential to the proper functioning of the submarine as q

whole.

L

.77.

Appendix K lists the most Important physical and psychological factors affecting crew

endurance. Submarine crews are an elite and dedicated group who are accustomed to

the close quarters of life aboard a submarine, but each man has his own tolerance level

for spartan conditions. Table 9-4

Hsts ship support and habitability parameters, many of which are only estimated from the

reference pictures of the submarines. The most Important parameter Is the volume-per-

man, given in cubic feet per man. WALRUS Is by far the most voluminously-appointed

vessel with 555 cubic feet/man, and MIDGET 100 Is by far the least with one fifth of that

value. The other boats are furnished with between approximately one-half to two-thirds

the volume per man as WALRUS. An examination of the days of provision loadout for

each vessel hints at the reasons for the great disparity In specific volumes - the mission

duration of WALRUS Is about five times that of MIDGET 100. Another explanation is

that different cultures have different levels of personal privacy needs, and the respective

shlpbuilders have reflected that in thier designs.

Of particular note Is that on BARBEL and SAURO, and MIDGET 100 as well, when

loaded with combat swimmers, some berthing Is located on the torpedo racks, whereas

the other submarines have all be ,ng located In designated berthing compartments.

Also, MIDGET 100 does not hay a mess room, although there is a space designated as

the galley/scullery.

8.5 Acoustic Countermeasures

Stealth and undetectability are essential for effective combat actions particularly for

diesel-electric submarines, which have a limited submerged range, and must be

indiscrete while recharging batteries. Diesel-electric boats are considered quieter than

nuclear boats when operating on battery, and there has been an intense effort by all

SHIP SUPPORT KILO WALRUS RUBIS BARBEL TYPESYSTEMS REF REF REF REF 2400 REF

TOTAL COMPLEMENT: 45 (17) 50 (24) 66 (8) 77 (17) 44 (32)OFFICERS: 15 (e) 7 (17) 9 (8) 8 (17) 7 (32)ENLISTED: 30 (e) 43 (17) 57 (8) 69 (17) 37 (32)

NR OF BERTHS 45 (e) 50 (e) 66 (10) 79 (35) 46 (32)NR OF LOCKERS 45 (e) 50 (e) 66 (10) 19 (35) 44 (32)NR OF MESS SEATS 25 (e) 40 (e) 32 (e) 26 (35) 26 (32)FRESH WTR, Lton 4.5 (e) 10 (e) 13.2 (e) 53 (34) 21.9 (32)EVAP PLNT, gal/day 450 (e) 1000 (e) 1320 (e) 924 (e) 840 (32)WTR, gal/man-day 10 (e) 20 (e) 20 (e) 12 (e) 19.09NR OF COMMODES 3 (e) 5 (e) 4 (e) 4 (35) 3 (32)AIR PURIFICATION YES (e) YES (23) YES (10) YES (35) YES (32)P-WAY WIDTH, (in) 30 (e) 36 (e) 32 (e) 28 (35) 33.7 (12)SHIP SUPPORT VOL: 14000 (e) 2775 2 (e) 15990 (e) 14562 (e) 11428 (e)SS VOL/MAN: 311.1 555.0 242.2 189.1 259.7PROVISIONS, Days 45 (e) 70 (7) 60 (10) 60 (e) 49 (17)

SHIP SUPPORT TYPE TYPE SAURO VASTER- MIDGETSYSTEMS 1700 REF 2000 REF REF GOTL'D REF 100 REF

TOTAL COMPLEMENT: 30 (8) 30 (5) 45 (12) 20 (36) 12 (33)OFFICERS: 8 (e) 7 (e) 7 (e) 7 (e) 4 (e)ENLISTED: 22 (e) 23 (e) 38 (e) 13 (e) 8 (e)

ONNR OF BERTHS 32 (8) 30 (e) 45 TORPS 20 (e) 8 (e)NR OF LOCKERS 32 (e) 30 (e) 45 (e) 20 (e) 12 (e)NR OF MESS SEATS 20 (e) 22 (e) 20 (e) 14 (e) 0 (e)FRESH WTR, Lton 6 (e) 6 (e) 9 (12) 3.78 (e) 0.96 (e)EVAP PLNT, gal/day 600 (e) 600 (e) 710 (12) 378 (e) 96 (e)WTR, gal/man-day 20 (e) 20 (e) 15.77 (11) 18 (e) 8 (e)NR OF COMMODES 3 (e) 4 (e) 2 (e) 2 (e) 2 (29)AIR PURIFICATION YES (e) YES (e) YES (11) YES (36) YES (29)P-WAY WIDTH, (in) 30 (e) 36 (e) 28 (e) 32 (e) 36 (e)SHIP SUPPORT VOL: 10043 10000 9817 7564 1265SS VOL/MAN: 334.7 333.3 218.1 378.2 105.4PROVISIONS, Days 70 (21) 70 (e) 45 (21) 30 (e) 14 (33)

Table 9-4: Ship support systems parameters.

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submarine manufacturers to reduce the sound emanation level as low as possible. with

the desired goal of being only as noisy as the ambient ocean. This is actually a variable

goal, since high sea-states are much noisier than low sea-states, and the silencing goal

has certainly been met on a number of submarines for higher sea-states.

Some of the more prevalent and unclassified methods of submarine silencing are shown

In Table 9-5. The use of propeller silencing, consisting of refinements in the

hydrodynamic shape of the propeller, resilient mounts for machinery, and a low speed

main shaft Is common to all the boats. Only KILO and TYPE 2400 employ anechoic hull

covering, and all boats except BARBEL have gearless main shaft drIves. These

parameters still only give qualitative indications of the silence of each submarine in

operation, since the effectiveness of the silencing methods is likely to vary among the

ships.

8.6 Survivability and Damage Control

A submarine Is inherently a warship. Because of Its limited volume and relatively high

cost per ton, there are few commercial ventures which would choose a submarine over a

surface displacement vessel. Being a warship, it must be expected that it shall be

required to venture into harm's way. The importance of stealth, silencing, first detection.

and first-strike capabilities have been discussed. The survivability shall now be

discussed.

In the event that a submarine is hit. the strength and toughness of its hull. and its

reserve bouyancy (ballast tanks) are the material-world determinants of its future.

Information on hull strengths and geometry of construction are not available in the

literature, but an estimate may be gleaned from knowledge of the immersion depth.

Appendix L lists several factors impotant to submarine vulnerability and survivability.

ACOUSTIC KILO WALRUS RUBIS BARBEL TYPECOUNTERMEASURES REF REF REF REF 2400 REF

RESILIENT MOUNTS YES (e) YES (17) YES (e) YES (e) YES (32)ANECHOIC HULL COVR YES (e) NO (e) NO (e) NO (e) YES (32)PROPELLER SILENCNG YES (e) YES (17) YES (e) YES (e) YES (32)LOW SPEED SHAFT YES (e) YES (e) YES (e) YES (e) YES (e)GEARLESS DRIVE YES (e) YES (e) YES (e) NO (17) YES (e)

TYPE TYPE SAURO VASTER- MIDGET1700 REF 2000 REF REF GOTL'D REF 100 REF

RESILIENT MOUNTS YES (e) YES (e) YES (12) YES (19) YES (29)ANECHOIC HULL COVR NO (e) NO (e) NO (e) NO (e) NO (e)PROPELLER SILENCNG YES (e) YES (e) YES (12) YES (19) YES (29)LOW SPEED SHAFT YES (e) YES (e) YES (12) YES (19) YES (29)GEARLESS DRIVE YES (e) YES (e) YES (12) YES (e) YES (29)

Table 9-5: Countermeasure outfit.

FLOODING KILO WALRUS RUBIS BARBEL TYPEPROTECTION REF REF REF REF 2400 REF

NR OF WT COMPTMTS 4 (e) 3 (e) 3 (e) 3 (e) 3 (e)VOLUME OF LARGEST 20000 (e) 26500 45930 18450 24720WT SPACE, cuftMBT VOLUME, cuft 24500 12250 9975 11340 8400

MBT/COMPT RATIO: 1.225 0.462 0.217 0.614 0.339


NR OF WT COMPTMTS 3 (e) 3 (e) 3 (e) 2 (36) 1 (e)VOLUME OF LARGEST 28923 26446 19300 19971 3370

WT SPACE, cuftMBT VOLUME, cuft 7350 9310 6300 2450 420

MBT/COMPT RATIO: 0.254 o.352 0.326 0. 122 0. 124

Table 9-6: C-ompartment measurements germane to damaged survivability.

. . m mi I I I i i

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Table 9-6 details calculations of reserve bouyancy limits in a scenario Involving flooding

to the single largest compartment of the submarine. In the event of flooding, the main

ballast tanks could be blown down, enabling the submarine to aviod sinking. The

"MBT/COMPT" ratio Is the fraction of the largest compartment volume which could be

flooded before 90% of the reserve bouyancy would be expended in attempting to keep

the submarine afloat. The favorite Is KILO, which because of its greater degree of

compartmentation and large ballast tanks, would be able to avoid sinking If damaged In

only one compartment. This Is not to say that KILO would remain mission-capable, or

that subsequent shots would cause more extensive and Irrecoverable damage. but all

the other submarines are clearly one-shot platforms.

The KILO is the most capable submarine of those in this study to withstand severe

damage. Its double-hull construction can withstand explosive warheads better than a

single-hulled submarine of equal test depth rating, because the outer hull prevents the

warhead from detonating as close to the pressure hull as it would have with a single-hull

design. Reference (27) provides some insight to additional possible reasons for the use

of double-hull designs by the U.S.S.R.:

The pitiful peacetime safety record of Soviet submarines suggests serious designflaws, inattention to safely, lack of crew/shipyard maintainance of onboard equipment,and poor seamanship. Given the propensity of Soviet submarines to collide withsubmerged and surface objects, it was probably a wise decision to continue buildingmore survivable doublehull submarines.

The bottom line of all this is that the capacity to withstand severe damage is certainly an

asset, but the ability to avoid any damage at all. due to superior stealth, sensor range,

weapon effectiveness, speed. and crew training state is a much greater asset.

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8.7 Escape and Rescue

Table 9-7 lists the submarine escape and rescue facilities. Note that all of the

submarines have been provided with at least one escape scuttle. The TYPE 1700 and

TYPE 2000 are also equipped with escape pods of large enough capacity to hold the

entire crew and provide them with four days sustalnance.

-- . i -------

CASUALTY KILO WALRUS RUBIS BARBEL TYPEPARAMETERS REF REF REF REF 2400 REF

BATTERYSEGREGATION? YES (e) NO (e) NO (e) NO (e) YES (e)DEGAUSSING YES (e) YES (e) YES (e) YES (e) YES (e)

ESCAPE AND RESCUEESCAPE SCUTTLE? YES (17) YES (23) YES (e) YES (e) YES (32)NUMBER OF SCUTTLES 2 (17) 2 (23) 2 (e) 2 (e) 2 (32)

ESCAPE POD ABOARD? NO (e) NO (e) NO (e) NO (e) NO (e)POD CAPACITY N/A (e) N/A (e) N/A (e) N/A (e) N/A (e)RESCUE BEACON? YES (e) YES (e) YES (e) YES (e) YES (e)

CASUALTY TYPE TYPE SAURO VASTER- MIDGETPARAMETERS 1700 REF 2000 REF REF GOTL'D REF 100 REF

BATTERYSEGREGATION? YES (e) YES (e) YES (e) NO (e) NO (e)DEGAUSSING YES (e) YES (e) YES (e) ERICCS(36) YES (e)

ESCAPE AND RESCUEESCAPE SCUTTLE? YES (2) YES (e) YES (e) YES (36) NO * (e)NUMBER OF SCUTTLES 1 (2) 1 (e) 1 (e) 1 (36) N/A (e)

ESCAPE POD ABOARD? YES (5) YES (5) NO (e) NO (e) NO (29)POD CAPACITY 30 (5) 30 (5) N/A (e) N/A (e) N/A (29)RESCUE BEACON? YES (e) YES (e) YES (e) YES (e) NO (29)

Table 9-7: Escape and Rescue capabilities.

,,,.,,m mm u ,~lmm m,, N a ~ lili imi p m - ° U

.84-

Chapter 9

COMPARATIVE NAVAL ARCHITECHTURE

9.1 Specific Volumes

Table 10-1 lists the values of the weights of the functional groups divided by the volumes

of the functional groups.

9.1.1 Mobility

For the mobility functional group. the weight/volume ratio seems to be related to thp

endurance range, with higher ratios occuring In submarines with shorter ranges. This is

because bunker fuel Is less dense than the propulsion machinery and battery, and the

large fuel loads required for long ranges drop the average weight of the entire functional

group.

9.1.2 Weapons Systems

The weight/volume ratios for the weapons systems are a function of how densely the

space Is packed with reload torpedoes. For MIDGET 100, the exceptionally high value

is due to the exceptionally small portion of the pressure hull devoted to weapons, since

the torpedoes are muzzle-loaded and there is no positive launching gear to take up

space either. The ratios for BARBEL and SAURO are comparable to the ratios of the

other subs because the volume over the torpedo racks used for berthing was charged to

the ship support group.

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COMPARATIVE KI LO WALRUS PUB I S BARBEL TYPEANAILYSIS --- 2---

Weight FractionsWmob/Dsub 2. 2182 0. 23277 . 40189 1 36161Wwep/Dsub 0. 02450) C. 01731 0. (,2003 C. .42 5 02497WC3i /Dsub f. U12'098 ,. 1793 5 0.. )1998 349

Wss/Dsub o.03146 0.C)3037 - 0. 047 3 S C) C) 4 '3 C). 0-4211

Speci fic Vo:lumesWmob/VOLm, ibs/,-uft 47.31 5316 2,. 9003 50. 0)321 5 J , 52.W96

Wwep/VOLw, lbs/cuft 17.5638 11.699 11.7750 19. 6652 1'.9672 IWc3i/VOL-, lbs,cuft 13.6764 19.0839 2C).2974 13.7195 20.6143Wss/VOLs, lbs/,uft 16. 1123 7. 91*767 17.7243 1'. 9975 19.8121

Propulsion Plant Density

Wmc,b/SHPi, lbs/HP 392. 137 330.893 24 0.364 408. 888 36z. 10

Ship Suppcrt Vol ume Per Crewmember'.!OLe/#C, cuft/man 311. 111 5.55 .0)4 242.272 139. 116 259.117

Indiscretion ParametersIncliscretn Rate @ 6 Kts k).S: 0.067 hA w. (74 0. 126Indiscretn Rate C Kt 0.3' C. 199 N/A C'. 227 C. 360Inoilcretn Intrvl @ 6 IKts.-..7 34. i N/A 46.c 36.7Indiscretn Intrvl @10 Kts 10.7 I .0 N/A 14.7 11.8

Range Capabilities

Bunker Fuel Range @ 6 Kts 14931 11227 1020 15735 8337Provision Range 3 6 Kts 5760 10080 8640 8640 7056Bunker Fuel Range @10 Kts 10713 7178 217 10993 5684Provision RanQe @10 ts * 96()C0 1630 14400 14400 11760

Endurnce Range @ 6 Kts, Nm 5760 I()80 3640 864o 7056Endurnce Range @110 Kts, Nm 960() 717 14400 9897 5221

Battery Range 3 6 [its, Nm 196 204 228(Battery Range @10 Kts, Nm 107 110 2147 11

Battery Range @18 Lts, Nm 29.4 9.- 5 -,.. 32.4Battery Range @25 Kts, Nm N/A N/A 1.5 N/f N/A

Calculated Max Speed 1S 25. I i.u 20.5

WEAPONS DELIVERY K I LO WALRUS FPUB I S EAREEL ECz:OMPAR I SON 24:);

W E P S i : .P b 1 .('# T ) ( # W t / 1 C 0)C , 5 . 4 ,C. , .. i . .,

WEPS2: F'6) (#Wc,),1000 ;.g4 _.. " ,,-

WEPS3: fR6) (#Wm, . 1 C'i3 6C)- ."7F CH '-P : Id , ma -' 2, , i' '' VJ' ' - ,. .

(Pb 1 C .#T.) #Wt., ' Dsub .. : . . . *I. - .

'FR6. #Wm.nDsub ' ' *" '.. " ' 1'.',',

T_--3beetcMp r , , v : m ,.5.... .: e r? tln! 9'.

-86-

COMPARATIVE TYPE TYPE SAURO VASTER- MIDGETANALYSIS 1700 2000 GOTLAND 100

Weight FractionsWmob/Dsub 0.42035 0.39551 0.32099 0.36846 0.24896Wwep/Dsub ). 01799 0.02512 0.04264 0.06862 0.11625Wc3i/Dsub 0.01380 0.01712 0.03703 0.03617 o.04295Wss/Dsub 0.02836 0.03253 0.04218 0.04333 0.06127

Specific VolumesWmob/VOLm, Ibs/cuft 44.2359 46.9153 50.2038 53.8030 79.2533Wwep/VOLw, lbs/cuft 16.6846 21.8591 18.4603 24.7112 87.4459Wc3i/VOLc, lbs,cuft 15.1227 16.8685 18.8881 19.2311 17.6129Wss/VOLs, ibs/cuft 14.8688 16.9795 15.9778 14.6297 14.7560

Propulsion Plant Density

Wmob/SHPi, lbs/HP 250.194 275.236 283.716 370.874 180.584

Ship Support Volume Per CrewmemberVOLs/#C, cuft/man 334.766 333.333 218.155 378.2 105.416

Indiscretn Rate @ 6 Kts 0.066 0.072 C).110 0.111 N/AIndiscretn Rate @10 Kts 0.187 0.197 0.309 0.313 N/AIndis,retn Intrvl @ 6 Kts 81.2 68.1 30.1 22.9 N/AIndiscretn Intrvl @10i Kts 27.9 24.3 10.) 7.6 N/A

Bunker Fuel Range @ 6 Kts 15039 12651 9115 3231 1345Provision Range @ 6 Kts 10080 12960 6480 4320 2016Bunker Fuel Range @10( Kts 10736 9293 6891 1956 819Provision Range @10 Kts 16800 21600 10800 7200 3360

Endurnce Range @ 6 fts, Nm 10080 12651 6480 3231 1345Endurnce Range @10 Kts, Nm 10736 9293 6891 1956 819

Battery Range @ 6 Kts, Nm 487 408 161 138 41Battery Range @10 Kts, Nm 279 243 100 76 20Battery Range @18 Kts, Nm 83.6 74.6 27.4 20.5 4.1Battery Range @25 Kts, Nm 36.0 32.1 N/A N/A N/A

Calculated Max Speed 24.7 25 19.3 20 16.8

WEAPONS DELIVERY TYPE TYPE SAURO VASTER- MIDGETCOMPARISON 1700 2000 GOTLAND 100

WEPSI: (Rbl))(#T)(#Wt)/()0(') 36.82 38.87 7.17 5.48 0.32WEPS2: (R6)(#W,:)/10(0)0 N/A N/A N/A N/A N/AWEPS3: (R6) (#Wm)/100C) 323 304 78 39 13ESCAPE: (Id) (Vma:, 2) 183027 731125 111747 1200) C 56448

(Rbl(:)* (#T' (#Wt)/Dsub 15.67 16.68 4.32 4.31 2.35(F'6')(#Wc)/DLb N/A N/A N/A N/A N/A(R,6)i (#Wm')/Dsub C0. 1 ('.1 C. C' 0 0. 1

Table 10-1: Comparison cof performance and design parameters.(Sheet two of two.'

-87-

9.1.3 Command, Control, Communications, and Information

All the ratios are about the same except for KILO, which is presumably lower due to the

extra volume taken up by the vacuum-tubes and the additional HVAC ducting needed to

maintain the temperature.

9.1.4 Ship Support

All of the values are about the same except for WALRUS, which has an exceptionally

large ship support volume. WALRUS apparently has been designed with extra volume

to allow greater crew comfort during the exceptionally long (70+ days) missions of which

this vessel Is capable. The empirical formula for ship support weight developed In

Appendix I Is a stronger function of complement than of vessel size.

9.2 Mobility Weight/Installed Power

An economy of scale Is evident in the ratio of mobility weight to Installed shaft

horsepower, with lower ratios occuring for higher SHPI, on vessels such as RUBIS,

TYPE 1700, and TYPE 2000. The low value for SAURO is due to Its densely-packed

engine room, a design trait for which Fincantleri Is well known.

9.3 Overall Endurance Ranges at Six and Ten Knots

Ten knots Is a reasonable speed for a diesel-electric submarine in transit to or from the

operating area. Six knots Is a reasonable speed for patrolling a choke-point operating

area. Overall endurance range at ten knots Is the fuel endurance range for the subject

submarines, and the overall endurance range at six knots is in general determined by

the provision endurance. Figure 10-1 shows a comparison of these ranges. The long

range of the nuclear-powered RUBIS at ten knots is of note, as is the short range of

": .==. -- -, n m. u a m in RN N m m m~1

MIDGET 100 at both speeds. MIDGET 100 may be towed to the operating area, but is

probably best at missions of shorter duration, as Is apparently also the case for TYPE

2400 and VASTERGOTLAND. VASTERGOTLAND was most likely designed to patrol

the coast of Sweden looking for KILO and other Soviet submarines, which have an

affinity for the fords. The other boats were probably designed for, and are capable of,

long range solo transits to and from a remote location, and with enough fuel and

provisions remaining to spend a healthy amount of time at the operating area.

9.4 Battery Endurance Range

Figure 10-2 shows a comparison of the battery ranges of each submarine at speeds of

six, ten, eighteen, and twenty-five knots. TYPE 1700 and TYPE 2000 are the best In this

area. They are also the only submarines to have appreciable battery range at twenty-

five knots, although RUBIS would be expected to go nuclear Its limited battery energy

was exhausted and It still needed to make that speed. Battery endurance range Is of

great combat significance, because the submarine Is much less detectable when on

battery than when snorkeling.

9.5 Indiscretion Rate and Interval

Once at the opearating area, the diesel-electric submarine will need to recharge Its

batteries from time to time. If operating In a war zone, low Indiscretion rate and long

Indiscretion Interval may be crucial to the submarine's combat effectiveness. With a long

Indiscretion Interval, the submarine skipper has the flexibility to choose the best time to

recharge batteries. Notification of that time could even come from a shore station or

other friendly units, based upon satellite Information or other sensor data.

Figures 10-3 and 10-4 show a comparison of the Indiscretion rates and Intervals at

- ~, -7'

-4-J

4-J

N-. C. tn 0 P% -0V

UJN '01 A

Figur 101 Coprsno vrlSnuac agsa

Six and Ten Knt . ~1

-90-

01,

C)

0 0

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0

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UN 'OODJD

Figure 10-2: Comparison of Battery Endurance Range at Sixand Ten Knots.

-91-

speeds of six and ten knots. Of immediate note is the fact that RUBIS and MIDGET 100

have zero indiscretion rates and Indefinitly long indiscretion Intervals, since neither of

them needs to snorkel in order to recharge batteries. TYPE 1700 and TYPE 2000 have

the next best ratings, due to their very large batteries and large diesel alternator sets.

9.6 Escape Capability

Figure 10-5

shows each submarine's rating on an arbitrary parameter designed to evaluate escape

capability once detected. The parameter places a premium upon top speed due to its

Importance In outrunning a torpedo. The parameter is the product of the immersion

depth and the square of the top submerged speed. Immersion depth Is Important

because Internal combustion propelled torpedoes have decreased range with Increased

depth. The high scorers are RUBIS, TYPE 1700, and TYPE 2000. The low ratings for

BARBEL, TYPE 2400, and MIDGET 100 are a result of their poor Immersion depth and

lower top speed.

9.7 Weapons Delivery Capabilities and Platform Efficiencies

9.7.1 Torpedoes

The ability to deliver ordnance on target is essential for combat effectiveness. For a

measure of overall torpedo delivery effectiveness, an arbitrary parameter is the product

of battery endurance range at ten knots, number of torpedo tubes, and number of

torpedoes carried. This product is then divided by 1000 for scaling. An arbitrary

parameter for the platform efficiency of torpedo delivery would be the same product

divided by submerged displacement. Figure 10-6 compares the calculated values of

these parameters.

-92-

/ / JIi i i / /-

V//. / */////* /,f/,," - V.// l/////// 2//t;.",

o /¢ "II X / .. / / / -"I"iJ" I

4--

Ylci .' /'' / .' / ,/',

. 2 . 1 / .i"." , ..- " . .,-

. , ".,., , L

I> .."

f . f b" f Y,

o '7 '7', /,./ "// /7i ' i .vE.

a *',,,,-,,,./ K .",.'.. 7(1 .. "\\, -".t

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ac

F 1i'3 Compais ofw Iiscret io/ Rt a/ S' ' ,"

r € 1 € f "." x"t J " _"-"b -N " "t"x

r

St*' * X ', // / **- ,.-" . ' ".,. ,. ..

.," f , i_/ I ' ' ," ," -"II I I I

Figure 10-3: Comparison of Indiscretion Rates at Six and Ten Knots.

-93-

2T:CE

~0

o -

~4rJ0

wo

o- . 03

o I/ ,

-0

cnoH 'IDAwS*4ulFigure 10-4: Comparison of Indiscretion Intervals at Six and Ten Knots.

-94-

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ap

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(VIQn-4>

(Z- XDJA)(P3

Figue 105: ompaiso 6f scap Caabilty aramter

-95-

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4 4

op

I (. . ? "

S -. , . ,I.

I.0 , _,- 5- .- .. ,-- . ,. ', .- ,- C,

f0.1 . /"S* I" i" 5. ... ... . S..5.. / I /" ,-"i ," -

S.. S.-, ",, S. " -,, ,. -,.-.,.

... \. \ -S... s"* S.."..'"S.. " i** < *.," .,-'

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Figure 10-6: Weapons Delivery arameter: Torpedoes andBattery Range at Ten Knots.

-96-

The high values for TYPE 1700 and TYPE 2000 are again a result of the outstanding

battery endurance range of those vessels, combined with their large torpedo loadout.

The low score for RUBIS Is not truly repesentatve of that submarine's combat

effectilveness, since reactor range at ten knots Is much greater, but Is Included for

comparison. The platform efficiencies of KILO, WALRUS, BARBEL, TYPE 2400,

SAURO, and VASTERGOTLAND are all Inthe same range, and the platform efficiency of

MIDGET 100 Is not much below that.

9.7.2 Cruise Missiles

For a measure of overall crulse missile delivery effectiveness, an arbitrarty parameter Is

the product of overall endurance range at six knots and the number of cruise missiles

carried. This product Is then divided by 1000 for scaling. An arbitrary parameter for the

platform efficiency of cruise missile delivery would be the same product divided by

submerged displacement. Figure 10-7 compares the calculated values of these

parameters. The overall endurance range at six knots is used because the stand-off

launch mode of the cruise missile does not require lengthy periods on battery as torpedo

attacks do, and instead, the emphasis should be placed upon endurance on station.

WALRUS stands out as the leader In this area because of its high weapons loadout

capacity and excellent slow-speed endurance range due to its high provision loadout.

TYPE 1700, TYPE 2000, SAURO, VASTERGOTLAND, and MIDGET 100 fail to score in

this area due to the inability of their torpedo tubes to launch cruise missiles. KILO,

RUBIS, BARBEL, and TYPE 2400 are all approximately equal in both overall capability

and platform efficiency.

,,-w,,, mm mMmammm mmm m mmm mW J mmmm mmm- I

CLIL

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Figue 1-7: Weapns eliery araete: CriseMisile

and~~~~~~~~ FulEdrneRngEtSxKos

-98-

9.7.3 Mines

For a measure of overall mine delivery effectiveness, an arbitrarty parameter Is the

product of overall endurance range at six knots and the number of rnines carried. This

product Is then divided by 1000 for scaling. An arbitrary parameter for the platform

efficiency of mine delivery would be the same product divided by submerged

displacement. Figure 10-8 compares the calculated values of these parameters. The

overall endurance range at six knots Is used to represent the degree of flexibility the

submarine would have In remaining on station to pick the best time to place the mines.

Actual placement of the mines would usually be conducted on battery.

WALRUS again leads the pack In this area due to Its high loadout of provisions for long

endurance and mines for combat effectiveness. TYPE 1700 and TYPE 2000 achieve

good scores as well, and have about the same platform efficiency as WALRUS.

MIDGET 100 Is next for platform efficiency, and might be even higher If the analysis

were to Include the contributions of the auxiliary mine pods which may be loaded

externally. The remaining boats are reasonably effective minelaying vehicles.

9.8 Conclusions

This study places a great deal of importance on speed and endurance range. The

author states that these are essential attributes for combat effectiveness, and are

suitable Indices of comparison in lieu of more subtle, or unavailable, parameters such as

sensor ranges, sound emanation profiles, equipment failure rates, or casualty control

needs.

The main conclusion to be drawn Is that automation of systems will allow a reduction of

crew size, which then permits a larger battery and greater provision, fuel, and weapons

loadouts. This will lead to greater combat effectiveness due to increased range, attack

flexibility, speed, and weapons delivery potential.

m

-99-

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tv

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14' *i

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Figure 10-8: Weapons Delivery Parameter: Mines and

Fuel Endurance at Six Knots.

m~m ,, m~m I* . c- iU

-100-

Chapter 10

AREAS FOR FURTHER STUDY

The following areas would Increase the depth of this study and enable a more

comprehensive comparison between the subject submarines.

10.1 Maneuvering Characteristics

The maneuvering capabilities of each submarine could be modeled and the results used

to develop tactical engagement and attack parameters and techniques.

10.2 Weight Distribution

The determination of weights and weight distributions of each system and functional

group needs to be accomplished. The weights calculated In this study are all based

upon the same empirical formulas, so the notion of comparing one submarine's weight

groupings to another's Is Impossible. It may be Impossible to publish a study of this

detail, since the actual values of submarine weight groups are often proprietary data, If

not classified.

10.3 Specific Fuel Consumption Increase at Snorkel

Many state-of-the-art diesel engines have SFC's in the low 0.30's (Ib/HP-Hr) when run

on the test bed. The additional fuel consumption Increase due to the flow restrictions in

the Intake and exhaust ducts could be accomplished. The result would Improve the

accuracy of the calculated endurance range. Additionally, a relation should be possible

between the Increase in SFC due to the length of the intake and exhaust trunks, and the

-101.

additional horsepower needed to operate close to the surface, so that an optimum sail

height for anticipated snorkeling speed could be found.

10.4 Hull Strength Estimation

A model of each submarine's pressure hull could be developed, and analyzed for actual

crush-depth estimate. Several of the submarines have the same published minimum

(normal) operating depth, how much safety factor (or military discretion) has been

employed In each? This model also probably could not be accomplished with much

accuracy with only open-literature sources.

10.5 Weapons and Sensors Capabilities

The focus of this study was comparative design of the marine engineering aspects of the

submarines. The weapons systems capabilities and the sensor ranges of each

submarine could be researched or estimated, and a more thorough evaluation of the

combat effectiveness of each submarine could be accomplished.

-102-

Chapter 11

REFERENCES

1. *Anaerobic Diesel-Powered Midget Submarine With Extended Non-Snorkel

Submerged Range", Maritime Defense, Volume 11, Number 4. April, 1986.

2. "Canadian Submarine Acquisition Program (CASAP)", Wings Magazine. Issue

devoted to Canada's Navy. Fall 1987.

3. Carmichael, A. Douglas. "Notes from MIT Course 13.21: Naval Ship Power and

Propulsion". Fall Term, 1987.

4. Coeshall, Bob. "Submarine Manoevering Control, Requirements of Modem Platform

Control". Maritime Defense, Volume 8, Number 4. April, 1983.

5. "Conventional Submarines - A Further Review". The Naval Architect. May, 1983.

6. "Diesel-Electric Submarines". Maritime Defense. Volume 10, Number 1. January.

1985.

7. "Diesel-Electric Submarines and Their Equipment". International Defense Review.

Supplement V/1986. 1986.

8. "Diesel-Electric Submarines - Thyssen Nordseewerke Launches First TR 1700 and

Wins Norwegian Order". Maritime Defense. Volume 7, Number 10. October, 1982.

9. Direction Des Constructions Navales. "SSN, 'RUBIS' CLASS, 'AMETHYSTE'

BATCH", Direction Des Constructions Navales. France, 1986. Manufacturer's

Brochure.

10. Direction Des Constructions Navales. "SSN. 'RUBIS' CLASS". Direction Des

Constructions Navales. France. September 1984. (Industrie Catalogues (1) 737.13.13).

-103-

11. FaIrplay Marine Diesel Engine Directory. Fairplay International Records and

Statistics. London, United Kingdom. 1980.

12. Fincantled, Cantled Navall Itallani S.p.A. "SAURO-Class Submarine". Fincantleri.

Cantleri Navall Itallani S.p.A., Italy, (undated). (Manufacturer's Brochure).

13. "HMS UPHOLDER. Type 2400", Navy International. Volume 92, Number 7.

July/August 1987.

14. Heggstad, Kare M. "Submarine Hulls of Titanium, the Soviet 'Alfa' Class - Fact or

Fiction". Maritime Defense. Volume 8, Number 4. April, 1983.

15. "The IKL Submarine Escape Sphere". Maritime Defense. Volume 11, Number 3.

March 1986.

16. Jackson, Harry, P.E., CAPT USN (Ret). "Submarine Design". Notes from Charles

Stark Draper/MIT Professional Summer Course. 1982.

17. Jane's Fighting Ships 1987-1988. Janes Publishing Company, Ltd. London.

England. 1987.

18. Jordan, John. "Netherlands' WALRUS Submarine Takes to the Water". Jane's

Defense Weekly. Volume 4, Number 19. November 9, 1985.

19. "Kockums Concentrates on Submarines". The Naval Architect. March. 1986.

20. Unden, David, Editor-in-Chief. "Handbook of Batteries and Fuel Cells". Mcgraw-Hill

Book Company. New York, 1984.

21. Lotus 1-2-3, Release 2. Lotus Developement Corporation. Cambridge. Mass.

22. NAVY International. Volume 89. Number 12. December, 1984.

23. Polmar. Norman. "Guide to the Soviet Navy", 3rd Edition. U.S. Naval Institute

Press. Annapolis. MD, 1983.

-104-

24. RDM Naval Engineering. "Naval Engineering", RDM Naval Engineering.

Rotterdam, The Netherlands, (undated). Manufacturer's Brochure.

25. "Soviet 'AKULA" Submarine In Close-Up". JANES Defense Weekly. Vol 7. Issue 7.

Feb 21, 1987.

26. "Soviet KILO Class Submarines for Poland and India". Military Technology. Vol 10.

Number 8. Aug 10, 1987.

27. "Soviet Sub Design Philosophy." Proceedings. U.S. Naval Institute. Annapolis.

MD. Volume 113, Number 10. Oct 1987.

28. Strang, Gilbert. "Introduction to Applied Mathematics". Wellesley-Cambridge

Press. Cambridge. Mass. 1986.

29. Sub Sea Oil Services. "GST Midget 100 MK1 OGP-27". Sub Sea OIl services of

Micoperi, S.p.A. Manufacturer's Brochure. (undated).

30. "The Swedish 'VASTERGOTLAND'-Cfass Submarine". Maritime Defense. Volume

8. Number 4. April. 1983.

31. "Thyssen Nordseewerke and the TR-1 700". Maritime Defense. Volume 8. Number

4. April 1983.

32. "Type 2400 Patrol Class Submarine". Vickers Shipbuilding and Engineering. Ltd.

England, July, 1981. Manufacturer's Brochure.

33. U.S. Navy. "A 100-Ton Submarine Design From Italy". Office of Naval Research.

Volume 20-86. 18 March, 1986.

34. U.S. Navy. "Final Weight Report for SS-580". U.S.N. Bureau of Ships. 27 August,

1959

35. U.S. Navy. "USS BARBEL Arrangement Drawings". BuShips Dwo

SS580-845-1702763. U.S.N. Bureau of Ships. 1959.

L.|

-105-

36. "Vastergotland Al 7 Type Submarines". International Forum for Martltime Power.

Naval Forces Issue. Number III. 1983.

37. Varta Corporation. "Quarter of a Century of Modern Submarine Battery

Technology". Maritime Defense. Volume 11, Number 3. March, 1986.

-A -

APPENDIX A: GEOMETRY CALCULATIONS FOR ESTIMATING SUBMARINECOMPARTMENT VOLUMES

In order to determine the internal volumes of the submarines tothe greatest degree possible, generic submarine hull componentswere modeled on a computer spreadsheet.

Since the pressure hull is composed primarily of cylynder sec-tions, truncated cones, and hemispheres, the computer modelingis as easy as summing the volumes of the component sections. Theformulas used to model these compont sections are as shown below.The formulas were input to a computer spreadsheet, Reference (21),to facilitate computations. This worksheet, "SECTOR3.WKI" isincluded on the following page.

CYLYNDER: Vol = 2*PI*R*L EQN A-i

L*R-2 (R-z) L*R*(R-z)CYLYNDER SECTION: Vol ---- *(ACOS --- )(---------), EQN A-2

2 R 2

TRUNCATED CONE: Vol = (PI/3) * L * [R-2 + R*r + r^2], EQN A-3

TRUNCATED CONE SECTION:

n iL*R-2 (R-iz) L*R*(R-iz)Vol ~- *(ACOS ------ ) ---------- , EQN A-4

i=l 2 R 2

A-i

-A2-

"SECTOR3.WKI" (MAY BE USED FOR SUBMARINE VOLUME CALCULATIONS)(ASSUMES THREE-DECK ARRANGEMENT SCHEME)

CALCULATES COMPARTMENT VOLUMES.SECTOR AREA = R^2(ACOS((R-H)/R)-(R-H)(SQRT(R^2-(R-H)^2)

CIRCLE RADIUS: (R) 13.6 (input) CIRCLE RADIUS: (R) 13.8 (input)TOPSECTOR HEIGHT: 20.48 (input) BOTMSECTOR HEIGHT: 2.936 (input)

(R-H): -6.68 (R-H): 10.864

TOPSECTOR AREA: 476.0334 BOTMSECTOR AREA: 34.09241

MID SECTOR AREA: 88.159004426

TOPCOMPT LENGTH: 23.487 (input) BOTMCOMPT LENGTH: 21.31 (input)TOPCOMPT VOLUME: 11180.59 BOTMCOMPT VOLUME: 726.5093

18.47409MIDCOMPT LENGTH: 46 (input) CYLYNDER LENGTH: 44MIDCOMPT VOLUME: 4055.314 CYLYNDER VOLUME: 26324.53===================== ==========CYLYNDER DISPL: 752.1295====-

-------------------------------------------------- YLYNDER DISPL: 752.1295 -----

VOLUME OF A TRUNCATED RIGHT-ANGLED CONE:DIMENSIONS:SMALL END RADIUS: r = 10.996LARGE END RADIUS: R = 13.772LENGTH: L = 7.79

VOLUME: V = 3768.981 (PI*L/3)*(R^2+r^2+rR)

VOLUME OF A CONE: (LARGE END AND LENGTH ONLY)VOLUME: V = 1547.248

APPENDIX B: NUMERICAL APPROXIMATION OF SUBMARINEWETTED SURFACE AREA

The calculation of the wetted surface area of the bare hull,sail, and appendages is crucial to being able to solve for theeffective horsepower required at various speeds. An accuratecalculation of the wetted surface is difficult because of thegenerally non-isometric drawings of the submarines in theliterature. Accuracy may be improved by using numerical modelingmethods. Such a method is used in the interpolating program"SPLIN500.WK1" on the following pages which uses cubic splinematrices to approximate the surface of a body of revolution,then numerically evaluates the surface area from the interpolatingpolynomials. The cubic spline technique is from Reference (28),and the program is implemented on Lotus 1-2-3 (Rel 2), of Reference(21). The inputs are the measured radii at evenly-spaced stations,and the overall length of the submarine, the outputs are a set ofstation slopes, interpolating third-order polynomials, and thesurface area of each section and the entire submarine as well.Table B-1 method should be used with caution, because although thecubic-spline method guarantees that the cubic interpolatingpolynomials, and their first and second derivatives, will becontinuous over the body, it cannot guarantee that the surfaceso generated will accurately represent the surface from whichthe radii were extracted.

Another numerical modeling scheme is presented as "HERMFAST.WK1".This model uses Hermite polynomials, also from Reference (28),to determine the cubic interpolating functions. The inputs tothis model are both the radii and slopes at sequential stations,and with the added information of the slopes, this model is ableto calculate the surface area to as accuarate as the input datafrom the reference drawing will allow. Stations need not be evenlyspaced either. As few as two station data inputs are possiblefor the model to work, but accuracy is improved with more stations.with a maximum of eleven input stations currently programmed. Theoutputs are interpolating polynomials, the section areas, and thewetted surface of the entire bare hull. An run of HERMFAST ispresented here, with the input values for TYPE 2400 input as anexample.

The wetted surface areas calculated by these models are accuatefor bodies of revolution, so corrections must be made to accountfor the deck, skeg, tumblehome, and any other protrusions.

The surface areas of the sail and the appendages are measured fromthe available photographs or diagrams in the literature as best aspossible.

B-i

I

-B2-

"SPLIN50O.WK1" USED TO CALCULATE SURFACE AREA OF A BODY OF REVOLUTIO

The inputs are the station radii. The outputs are cubic- interplatipolynomials which form a curve which has continuous first and secondderivatives. CAUTION: The resultant body may n,:,t adequately model tgeometry of the actual body, since station slopes are not specified'

(USES CUBIC SPLINE MATRICES, FROM STRANG, pp 177-180.)

PROCEDURE:(1) INPUT ACTUAL LENGTH AND RADI I AT THE ELEVEN (EQUALLY-SPACED) STA(2) HIT [F9] TO CALCULATE.(3) MULTIPLY THE MATRIX AT K32 BY THE MATRIX AT W32, RESULT TO Y32.(4) HIT IF9) AGAIN TO GET SLOPES, INTERPOLATING COEFFICIENTS, AND AR

INPUTS: OUTPUTS:ACTUAL NORMALIZEDLENGTH: LENGTH: STATION SPAC:ING: -- 1

10 1n (1 amda')ACTUAL NORMALI ZED SURFA:E

STATION: RADIUS: RADIUS: SLOPE AT STATION: AREA) 0 C) SO: -4. 1E-181 C) C) 1: 8.2E-18 3.2E-18

0 C) 62: -1.OE-16 5.8E-173 0 0 63: -1.1E-16 4.1E-174 1 1 S4: 3 3.5634415 4 4 65: 1.OE-17 51.212516 1 1 S6: -3 51.212517 C) C) S7: 1.2E- 16 3. 5634418 0 C) Se: 6.IE-17 4.2E-179 0 C) $9: -1.9E-17 4. 1E-17

10 C) SI: 9.3E-18 1.5E-17

OUTPUT: COEFF. OF (NORMALIZED) INTERPOLATING POLYNOMIALS, U(0.a b c d

0 tc, 1: 4.1E-18 C) -4. 1E-18 0 SURFACE1 to 2: -9.4E-17 3.7E-16 -4.5E-16 1.7E-16 AREA:2 to 3: 1.6E-15 1.6E-15 -3.9E-15 3.1E-15 (model)3 to 4: 1 -9 27 -27 1C) 9.55194 to 5: -3 39 -165 .235 t:, 6: 3 -51 285 -521 (actual.)6 to 7: -1 21 -147 343 1'9.55197 to 8: 1.BE-16 -4.)E-15 3.0E-14 -7.6E-14B to 9: 4.2E-17 -I.IE-15 9.8E-15 -2.9E-149- 10: -9.3E-18 2.8E-16 -2.8E-15 9.2E-15

'NORMAL -- ) 3 1

-B3-OUTPUT: COEFF. OF (ACTUAL) INTERPOLATING POLYNOMIALS, U(X).

A B C D0 to 1: 4.1E-18 Q -4.1E-18 0 LAMDA:1 to 2: -9.4E-17 3.7E-16 -4.5E-16 1.7E-16 12 to 3: 1.6E-15 1.6E-15 -3.9E-15 3.1E-153 to 4: 1 -9 27 -274 to 5: -3 39 -165 2295 to 6: 3 -51 285 -5216 to 7: -1 21 -147 3437 to 8: 1.8E-16 -4.OE-15 3.0E-14 -7.6E-148 to 9: 4.2E-17 -1.1E-15 9.8E-15 -2.9E-149- 10: -9.3E-18 2.BE-16 -2. BE-15 9.2E-15

(ACTUAL -- > "X") X"3 X"2 X

RELATIONS: LET lamda = 1THEN: X = I*xAND: U(X) = I-U ',)THEREFORE A = a/ I

B = b/1

C = c

D = d*l

2 1 0 0 0 0 0 0 0 0 01 4 1 0 0 0 0 0 0 ) 00 1 4 1 0 0 0 0 0 0 00 0 1 4 1 0 0 0 0 C) 0o 0 0 1 4 1 0 0 o 0 00 0 0 0 1 4 1 0 0 C) 00 0 C) 0 0 1 4 1 C) C 00 0 0 0 0 0 1 4 1 C) 00 0 C) 0 o 0 1 4 1 00 0 0 o 0 o 0 1 4 10 o o 0 0 0 0 0 0 1 2

(11>×11 CUBIC SPLINE SLOPE MATRIX.)[A]

0.577 -0. 15 0.041 -0.01 0.002 -0. 00 0. 000 -0.00 0.00C)0)15 -0. C0 000-0. 15 0.309 -0. C)8 0. 022 -0. C) QC) . 0 1 -C). C)(0 0). 0(0) ) -C).003 ).000 -0. 000. 041 -0.08 0. 290 -0. 07 0. 02:) -o.00 0. 00 1 -. c(: €). 000107 -0. 00 0. 000-0. 01 0.)22 -0. :)7 0.283 -0.0)7 C). 020 -0.00 ). 0:)01 -C:). 00040 0. 000 -0.00C). C02 -) -0.00 0. 020 --C. 07 0. 288 -0. 07 0. o20 -0. 00 0.0 C)0 1495 --0.00 0.-0. 0)0 0.001 -0.00 0c).020,: -0.:)7 0. 288 -0.07 C). :)20 -0. :):)55 0. C) 001 -0 . 00

. oc)0 -0. (:C)0 .€1 -0) C .020 -0. :)7 0.268 --. 07 0. 003: -0. 00 0. 002-0).00 0.0():) -C).0 0. 01 -0. f0 0.)2:) -0.07 0. 238 -).07774 0.022 --0.010. 00 . )- 00 0.0C) J - . C)0.:)7 .. 29 0163 -C.08 0. 041-0. 00 0.000 -0.00 0. 000 -0.00 0.001 -0. 0. 022 -0. 08290 0. 309 -0. 150.000 -0.00 0. c:) -u.0C)) 0. Cc) -0.0 0. 2 --0. c)1 . 041451 -0. 15 0.577

(INVERTED 1ii,:II MAITRIX FROM ABOVE. :

-B4-

THE FORMULA FOR CALCULATING THE SPLINE FUNCTIONS:

CA]^-I x 3[U3 = IS]

[U] IS THE INPUT MATRIX[S] IS THE RESULTING SLOPE MATRIX[A] IS THE CUBIC SPLINE SLOPE MATRIX

0 -4.1E-180 8.2E-180 -1.OE-163 -1. 1E-1612 3C.) 1.OE-17

-12-3-3 1.2E-16' 6.IE-170 -1.9E-170 9.3E- 18

[U] [S]

-B5-

a b - d -0TO1SUB- 0 ****** 0- ------------------------------------STATION ------------------------ AVG SURFNUMBER: x^3 x'2 x"l x.0 U(x') L(i) RADIUS AREA

0 0 0 0 1 00.02 0.000 0.000 0.02 1 -8.2E-20 0.01 4.1E-20 2. 6E-210.04 0.000 0.001 0.04 1 -1.6E-19 0.01 1.2E-19 7.7E-210.06 0.000 0.003 0.06 1 -2.4E-19 0.01 2.0E-19 1.3E-200.08 0.000 0.006 0.08 1 -3.2E-19 0.01 2.8E-19 I.BE-200.1 0.001 0.01 0.1 1 -4.OE-19 0.01 3.6E-19 2.3E-20

0.12 0.001 0.014 0.12 1 -4.8E-19 0.01 4.4E-19 2.BE-200.14 0.002 0.019 0.14 1 -5.6E-19 0.01 5.2E-19 3.3E-200.16 0.004 0.025 0. 16 1 -6.4E-19 0.01 6.OE-19 3.8E-200 18 0.005 0. 0.32 0. 18 1 -7.1E-19 0.01 6.7E-19 4. 2E-20

0. ' .008 0.04 0.2 1 -7.8E- 19 0.01 7.5E-19 4. 7E -200.22 0. 010 0.048 0.22 1 -8.6E-19 0.01 8.2E-19 5. 2E -2C)24 0.013 0. 057 0.24 1 -9.2E-19 0.01 8.9E-19 5.6E-200.26 0.017 0.067 C). 26 1 -9.9E-19 0.01 9.6E-19 6.0E-200. 8 0. 021 0.078 0.28 1 -1. 1E-18 0. C0 1 1.oE-18 6.4E-20

0.31 0. 027 0. 09 0.3 1 -I.IE-18 0.01 1.IE-18 6. BE-2-..33 C ).032. 1C2 0.32 1 -1.2E-18 0.01 1. 1E-18 7. 2E -2

0.34 0.039 0.115 0.34 1 -1.2E-18 0.01 1.2E-18 7.5E -20.36 0. 046 0. 129 0.36 1 -1.3E-18 0.01 1.3E-18 7.9E -200.38 0.054 0.144 0.38 1 -1.3E-18 o.01 1.3E-18 8.2E-200.4 0.064 0.16 0.4 1 -1.4E-18 0.) I 1.4E-18 8.5E-20

0.42 0.074 0.176 0.42 1 -1.4E-18 0.01 1.4E-16 8.E-2 00.44 0. 085 0.193 0.44 1 -1.4E-18 0.01 1.4E-18 9.0E-200.46 0. 097 C..211 0.46 1 -1.5E-18 0.01 1.5E-18 9.2E-200.48 0.110 0.23) 0.48 1 -1.5E-18 0.01 1.5E-18 9.4E-20

0).5 0.125 0.25 0.5 1 -1.5E-18 0.01 1.5E-18 9.6E-200.52 0.140 0.27:) 0.52 1 -1.6E-18 0.01 1.5E-l 9.7E-200.54 0.157 0.291 0.54 1 -1.6E-18 0.01 1.6E-18 9.8E-200.56 o.175 0.313 0).56 1 -1.6E-18 0.01 1.6E-18 9.BE-200.58 0.195 0.336 0.58 1 -1.6E-18 0.01 1.6E-18 9.9E-200.6 0.-216 0.36 0.6 1 -1.6E-18 0.01 1.6E-18 9.9E-20

0.62 0.238 0.384 0.62 1 -1.6E-18 0.01 1.6E-18 9.BE -200.64 C).262 C).409 C).64 1 -1.5E-18 0.01 1.6E-18 9.7E-200.66 0.287 0.435 0.66 1 -1.5E-18 0.01 1.5E-18 9.6E-200.68 0.314 C).462 0.68 1 -1.5E-18 0.01 1.5E-18 9.5E-20o.7 0.343 0.49 0.7 1 -1.5E-18 0.01 1.5E-18 9.3E -20

0.72 0.373 0.518 0. 7.72 1 -1.4E-18 0.01 1.4E-18 9.OE-200.74 0.405 0.547 0.74 1 -1.4E-18 0.01 1.4E-18 8.7E-2C)0.76 0.438 0.577 0.76 1 -1.3E-18 0.01 1.3E-18 8.4E-200.78 0).474 0.608 0.78 1 -1.2E-18 0.01 1.3E-18 8.OE-200.8 C. 512 C). 64 0.8 1 -1.2E-18 0.01 1. 2E-18 7. GE- 20

0.82 0.551 0).672 0.82 1 -1.1E-18 0.01 1.1E-18 7.1E-200.84 0.592 0.7o5 C). 84 I -1. OE-18 0.01 1. 1E-18 6. 6E -200.86 0.636 C).739 C).86 1 -9.2E-19 0.01 9.6E-19 6.CE -2C).88 0.681 0.774 0.88 1 -8. 1E-19 0.01 3.6E-19 5.4E -2

C). 9 C.729 c). 81 C.9 1 -7. OE-19 c). 01 7.5 E-19 4.7 E C.0c:).92 0).778 0.846 0.92 1 -5.8E-19 C).()1 6.4E-19 4.C0E- 20.94 0. 830 0.883 0.'94 1 -4.5E-19 0.01 5. 1E-19 3. 2E-o0.96 0.384 0.921 C). 96 1 -3. IE-19 0.01 3. 8E-19 2. 4E-200.98 0. 941 6.960 0.98 -. 6E-19 0.01 2.3E-19 1. 5E-20

1 i 1 1 C) 0. C1 7. 9E-20 5. C)E-- 1

TOTAL: 3.2E- 1.

-B6-

a b c d I T0 2

SUB- -- -- ------------- ---

STATION AVG SURFNUMBER: x^3 x'2 x.l x"0 U(x) L(i) RADIUS AREA

1 1 1 1 1 01. 02 1.061 1. 040 1.02 1 2.OE-19 0. 02 9. 9E-20 I 2E-201.04 1.124 1.081 1.04 1 4.6E-19 0.02 3.3E-19 4.1E-2C)

1.06 1.191 1.123 1.06 1 7.8E-19 0.02 6.2E-19 7.8E-201.08 1.259 1.166 1.08 1 1.2E-18 0.02 9.7E-19 1.2E-191.1 1.331 1.21 1.1 1 1.6E-18 0.02 1.4E-18 1.7E-19

1.12 1.404 1.254 1.12 1 2.1E-18 0.02 1.8E-18 '.3E-19

1.14 1.481 1.299 1.14 1 2.6E-18 0.02 2.3E-18 2.9E-19

1.16 1.560 1.345 1.16 1 3.1E-18 0.02 2.8E-18 3.6E-19

1.18 1.643 1.392 1.18 1 3.7E-18 .0o2 3.4E-18 4.3E-19

1.2 1.728 1.44 1.2" 1 4.3E-18 0.02 4.OE-18 5.COE-19

1.2.. 1.815 1.488 1 ..22 1 5.OE-18 0.02 4.6E-18 5.8E-19

1.24 1.906 1.537 1.24 1 5.6E-18 0.02 5.3E-18 6.6E-19

1.26 2.000 1.587 1.26 6.3E-18 0.02 6.oE-18 7.5E-19

1.26 2.097 1.638 1.28 1 7.OE-18 0.02 6.6E-18 8.3E-19

1.3 2.197 1.69 1.3 1 7.7E-18 0.02 7.3E-18 9.2E-191.32 2.299 1. 742 1.32 1 8.3E-18 0.02 8.OE-18 1. OE- 181.34 2.406 1.795 1.34 1 9.0E-18 0.0:)2 8.7E-18 1.1E-18

1.36 2.515 1.849 1.36 1 9.7E-18 0.02 9.4E-16 1.2E-1B

1.38 2.628 1.904 1.38 1 1.OE-17 0.02 1.OE-17 1.3E-18

1.4 2.744 1.96 1.4 1 1.1E-17 0.02 1.1E-17 1.3E-18

1.42 2.863 2.016 1.42 1 1.2E-17 0.02 1.1E-17 1.4E-18

1.44 2.985 2.073 1.44 1 1.2E-17 0.02 1.2E-17 1.5E-18

1.46 3.112 2.131 1.46 1 1.3E-17 0.02 1.3E-17 1.6E-18

1.48 3.241 2.190 1.48 1 1.3E-17 0.02 1.3E-17 1.6E-18

1.5 3.375 2.25 1.5 1 1.4E-17 0.02 1.4E-17 1.7E-18

1.52 3.511 2.310 1.52 1 1.4E-17 0.02 1.4E-17 1.8E-18

1.54 3.652 2.371 1.54 1 1.5E-17 0.02 1.4E-17 1.8E-18

1.56 3.796 2.433 1.56 1 1.5E-17 0.02:, 1.5E-17 I.9E-18

1.58 3.944 2.496 1.58 1 1.5E-17 0.02 1.5E-17 1 E- 18

1.6 4.096 2.56 1.6 1 1.6E-17 0.02 1.5E-17 1 E- 18

1.62 4.251 2. 624 1.62 1 1.6E-17 0.2 l.6E-17 2. OE- 18

1.64 4.410 2.689 1.64 1 1.6E-17 0.02 1.6E-17 .OE -18•

1.66 4.574 2.755 1.66 1 1.6E-17 0.02 1.6E-17 27 OE- 181.68 4.741 2.822 1.68 1 1.6E-17 0.02 1.6E-17 2.0E-18

1.7 4.913 2.89 1.7 1 1.6E-17 0 .2 .6E-17 2OE- 18

1.72 5.088 2.958 1.72 1 1.5E-17 0.02 1.5E-17 1.9E-181.74 3.268 3.027 1.74 1 1.5E-17 0.02 1.5E-17 1.9E-181.76 5.451 3.097 1.76 1 1.5E-17 0. 02 1.5E-17 1.9E-181.78 5.639 3.168 1.78 1 1.4E-17 0.02 1.4E-17 1.8E-181.8 5.832 3.24 1.8 1 1.3E-17 .02 1.4E-17 1.7E-18

1.82 6.028 3.312 1.82 1 1.3E-17 0.02 1.33E-17 1.6E-181.84 6.229 3.385 1.84 1 1.2E-17 .02 1.2E-17 1.5E-181.86 6.434 3.459 1.86 1 i.IE-17 C..'02 1.1E-17 1.4E-18

1.88 6.644 3.534 1.88 1 9.6E-18 (.02 1.(E-17 1.3E-181.9 6.859 3.61 1.9 1 8.4E-18 .02 'D.0E-18 i.IE-18

1.92 7.077 3.686 1.92 1 7.OE-18 C) (1 7.7E-18 .6E-.191.94 7.301 3.763 1.94 1 5.5E-18 C0 6.2E-18 7.8E-191.96 7.529 3.841 1.96 1 3.8E-18 0.02 4.6E-18 5.BE-191.98 7. 762 3.920 1.98 1 2.0E-18 0.C2 2.9E-1 3.6E-19

C8 4 2 0 0.02 9.9E-19- 1.2E-I9

TOTAL: 5.8E-17

-B7-

a b c d 2 TO 3SUB- ************************STATION AVG SURFNUMBER: x'3 x'2 x.l x"O U(x) Li) RADIUS AREA

2 8 4 2 1 02.02 8.242 4.080 2.02 1 -1.9E-18 0.02 9.6E-19 1.2E-192.04 8.489 4.161 2.04 1 -3.6E-18 0.02 2.8E-18 3.5E-192.06 8.741 4.243 2.06 1 -5.1E-18 0.02 4.3E-18 5.5E-192.08 8.998 4.326 2.08 1 -6.3E-18 0.02 5.7E-18 7.2E-192.1 9.261 4.41 2.1 1 -7.3E-18 0.02 6.8E-18 8.6E-19

2.12 9.528 4.494 2.12 1 -8.2E-18 0.02 7.8E-18 9.7E-192.14 9.800 4.579 2.14 1 -8.8E-18 0.02 8.5E-18 1.1E-182.16 10.0)7 4.665 2.16 1 -9.3E-18 0.02 9. QE-18 1.1E-182.18 10.36 4.752 2.18 1 -9.6E-18 0.02 9.4E-18 1.2E-182.2 10.64 4.84 2.2 1 -9.7E-18 0.02 9.6E-18 1.2E-18

2.22 10.94 4.928 2.22 1 -9.7E-18 0.02 9.7E-18 1.2E-182.24 11.23 5.017 2.24 1 -9.5E-18 0.02 9.6E-18 1.2E-182.26 11.54 5.107 2.26 1 -9.3E-18 '.02 9.4E-18 1.2E-182.28 11.85 5.198 2.28 1 -8.BE-18 0.02 9.1E-18 1.1E-182.3 12.16 5.29 2.3 1 -8.3E-18 0.0(2 6.6E-18 1.1E-18

2.32 12.4 8 5.382 2.32 1 -7.7E-18 0.02 8.OE-18 1.OE-182.34 12.81 5.475 2.34 1 -7.0E-18 0.02 7.4E-18 9.3E-192.36 13.14 5.569 2.36 1 -6.3E-18 0.02 6.6E-18 8.4E-192.38 13.48 5.664 2.38 1 -5.4E-18 0. 2 5.BE-18 7.3E-192.4 13.82 5.76 2.4 1 -4.5E-18 0.02 5.0E-18 6.2E-19

2.42 14.17 5.856 2.42 1 -3.6E-18 0.02 4.OE-18 5. 1E-192.44 14.52 5.953 2.44 1 -2.6E-18 0.02 3.1E-18 3.9E-192.46 14.88 6.051 2.46 1 -1.6E-18 0.02 2.1E-18 2.6E-192.48 15.25 6.150 2.48 1 -5.2E-19 0.02 1.OE-18 1.3E-192.5 15.62 6.25 2.5 1 5.3E-19 0.02 6.1E-21 7.7E-222.52 16.00 6.350 2.52 1 1.6E-18 (.02 1.1E-18 1.3E-192.54 16.38 6.451 2.54 1 2.6E-18 0.02 2.1E-18 2.6E-192.56 16.77 6.553 2.56 1 3.6E-18 0.02 3.1E-18 3.9E-192.58 17.17 6.656 2.58 1 4.6E-18 0.02 4.1E-18 5.2E-192.6 17.57 6.76 2.6 1 5.5E-18 0.02 5.1E-18 6.4E-192.62 17.98 6.864 2.62 1 6.4E-18 0.02 6.OE-18 7.5E-192.64 18.39 6.969 2.64 1 7.2E-18 0.02 6.8E-18 8.6E-192.66 18.82 7.075 2.66 1 8.0E-18 0.02 7.6E-18 9.6E-192.68 19.24 7.182 2.68 1 8.7E-18 0.02 8.3E-18 1.OE-182.7 19.68 7.29 2.7 1 9.2E-18 0.02 8.9E-18 1. 1E-18

2.72 20.12 7.398 2.72 1 9.7E-18 0.02 9.5E-18 1.2E-182.74 20.57 7.507 2.74 1 I.OE-17 0.02 9.9E-18 1.2E-182.76 21.02 7.617 2.76 1 1.OE-17 0.02 1.OE-17 1.3E-182.78 21.48 7.728 2.78 1 1.OE-17 0.02 1.cE-17 1.3E-182.8 21.95 7.84 2.8 1 1.OE-17 0.02 1.OE-17 1.3E-18

2.82 22.42 7.952 2.82 1 I.OE-17 0.02 1.OE-17 1.3E-182.84 22.90 8.065 2.84 1 9.8E-18 0.02 I.OE-17 1.3E-182.86 23.39 8.173 2.86 1 9.3E-18 0.02 9.6E-18 1.2E-132.88 23.88 8.294 288 1 8.6E-18 0.029.0E-10 1.1E-182.9 24.38 8.41 2.9 1 7.7E-13 0.02 9.2E-18 i.COE--18

2.92 24.89 0.526 2.92 1 6.6E-18 0.02 7.2E-18 9.0E-192.94 25.41 8.643 2.94 1 5.3E-13 (.02 6.0E-18 7.5E-192.96 25.93 8.761 2.96 1 3.8E-18 0.02 4.5E-18 5.7E-192.98 26.46 8.880 2.98 1 2.OE-i8 0.02 2.9E-18 i.GE-19

3 27 9 i 0 0.02 1. OE-18 1.3E- 19

-OTAL: 4.iE- 7

-B8-

a b c d 3 TO 4SUB- 1 -9 27 -27- ------------------------------------STATION AVG SURFNUMBER: x^3 x^2 x^l xÔ U(x) L(i) RADIUS AREA

3 27 9 3 1 1.OE-153.02 27.54 9.120 3.02 1 0.000008 0.020000 0.000004 0.0000003.04 28.09 9.241 3.04 1 0.000064 0.020000 0.000036 0.0000043.06 28.65 9.363 3.06 1 0.000216 0.020000 0.00014 0.0000173.08 29.21 9.486 3.08 1 0.000512 0.020002 0.000364 0.0000453.1 29.79 9.61 3.1 1 0.001 0.020005 0.000756 0.0000953.12 30.37 9.734 3.12 1 0.001728 0.020013 0.001364 0.0001713.14 30.95 9.859 3.14 1 0.002744 0.020025 0.002236 0.0002813.16 31.55 9.985 3.16 1 0.004096 0.020045 0.00342 0.0004303.18 32.15 10.11 3.18 1 0.005832 0.020075 0.004964 0.0006263.2 32.76 10.24 3.2 1 0.008 0.020117 0.006916 0.0008743.22 33.38 10.36 3.22 1 0.010648 0.020174 0.009324 0.0011813.24 34.01 10.49 3.24 1 0.013824 0.020250 0.012236 0.0015563.26 34.64 10.62 3.26 1 0.017576 0.020348 0.0157 0.0020073.28 35.28 10.75 3.28 1 0.021952 0.020473 0.019764 0.0025423.3 35.93 10.89 3.3 1 0.027 0.020627 0.024476 0.003172

3.32 36.59 11.02 3.32 1 0.032768 0.020815 0.029884 0.0039083.34 37.25 11.15 3.34 1 0.039304 0.021040 0.036036 0.0047643.36 37.93 11.28 3.36 1 0.046656 0.021308 0.04298 0.0057543.38 38.61 11.42 3.38 1 0.054872 0.021621 0.050764 0.0068963.4 39.30 11.56 3.4 1 0.064 0.021984 0.059436 0.008210

3.42 40.00 11.69 3.42 1 0.074088 0.022400 0.069044 0.0097173.44 40.70 11.83 3.44 1 0.085184 0.022871 0.079636 0.0114443.46 41.42 11.97 3.46 1 0.097336 0.023402 0.09126 0.0134193.48 42.14 12.11 3.48 1 0.110592 0.023994 0.103964 0.0156733.5 42.87 12.25 3.5 1 0.125 0.024649 0.117796 0.0182433.52 43.61 12.39 3.52 1 0.140608 0.025369 0.132804 0.0211693.54 44.36 12.53 3.54 1 0.157464 0.026155 0.149036 0.0244923.56 45.11 12.67 3.56 1 0.175616 0.027009 0.16654 0.0282623.58 45.88 12.81 3.58 1 0.195112 0.027930 0.185364 0.0325293.6 46.65 12.96 3.6 1 0.216 0.028918 0.205556 0.037350

3.62 47.43 13.10 3.62 1 0.238328 0.029975 0.227164 0.0427843.64 48.22 13.24 3.64 1 0.262144 0.031099 0.250236 0.0488973.66 49.02 13.39 3.66 1 0.287496 0.032291 0.27482 0.0557583.68 49.83 13.54 3.68 1 0.314432 0.033549 0.300964 0.0634413.7 50.65 13.69 3.7 1 0.343 0.034873 0.328716 0.072026

3.72 51.47 13.83 3.72 1 0.373248 0.036262 0.358124 0.0815953.74 52.31 13.98 3.74 1 0.405224 0.037715 0.389236 0.0922383.76 53.15 14.13 3.76 1 0.438976 0.039232 0.4221 0.1040503.78 54.01 14.28 3.78 1 0.474552 0.040812 0.456764 0.1171283.8 54.87 14.44 3.8 1 0.512 0.042454 0.493276 0.131579

3.82 55.74 14.59 3.82 1 0.551368 0.044156 0.531684 0.1475133.84 56.62 14.74 3.84 1 0.592704 0.045920 0.572036 0.1650463.86 57.51 14.89 3.86 1 0.636056 0.047743 0.61438 0.1843003.88 58.41 15.05 3.88 1 0.681472 0.049624 0.658764 0.2054033.9 59.31 15.21 3.9 1 0.729 0.051564 0.705236 0.228489

3.92 60.23 15.36 3.92 1 0.7786688 0.053562 0.753844 0 .2536993.94 61.16 15.52 3.94 1 0.830584 0.055616 0.804636 0.2811793.96 62.09 15.68 3.96 1 0.884736 0.057727 0.85766 0.3110823.98 63.04 15.84 3.98 1 0.941192 0.059893 0.912964 0.343570

4 64 16 4 1 1 0.062115 0.970596 0.378809

TOTAL: 3.563441

a b c d 4 TO 5SUB- -3 39 -165 229STATION AVG SURFNUMBER: x^3 x^2 xl xÔ U(x) L(i) RADIUS AREA

4 64 16 4 1 14.02 64.96 16.16 4.02 1 1.061176 0.064362 1.030588 0.4167694.04 65.93 16.32 4.04 1 1.124608 0.066510 1.092892 0.4567154.06 66.92 16.48 4.06 1 1.190152 0.068527 1.15738 0.4983344.08 67.91 16.64 4.08 1 1.257664 0.070412 1.223908 0.5414724.1 68.92 16.81 4.1 1 1.327 0.072162 1.292332 0.5859594.12 69.93 16.97 4.12 1 1.398016 0.073778 1.362508 0.6316094.14 70.95 17.13 4.14 1 1.470568 0.075258 1.434292 0.6782204.16 71.99 17.30 4.16 1 1.544512 0.076601 1.50754 0.7255764.18 73.03 17.47 4.18 1 1.619704 0.077806 1.582108 0.7734484.2 74.08 17.64 4.2 1 1.696 0.078873 1.657852 0.8215964.22 75.15 17.80 4.22 1 1.773256 0.079802 1.734628 0.8697704.24 76.22 17.97 4.24 1 1.851328 0.080593 1.812292 0.9177104.26 77.30 18.14 4.26 1 1.930072 0.081244 1.8907 0.9651494.28 78.40 18.31 4.28 1 2.009344 0.081756 1.969708 1.o118164.3 79.50 18.49 4.3 1 2.089 0.082128 2.049172 1.057430

4.32 80.62 18.66 4.32 1 2. 168896 0.082361 2.128948 1.1017114.34 81.74 18.83 4.34 1 2.248888 0.082454 2.208892 1.1443734.36 82.88 19.00 4.36 1 2.328832 0.082407 2.28886 1.1851334.38 84.02 19.18 4.38 1 2.408584 0.082221 2.368708 1.2237054.4 85.18 19.36 4.4 1 2.488 0.081895 2.448292 1.259807

4.42 86.35 19.53 4.42 1 2.566936 0.081430 2.527468 1.2931574.44 87.52 19.71 4.44 1 2.645248 0.080825 2.606092 1.3234824.46 88.71 19.89 4.46 1 2.722792 0.080081 2.68402 1.3505124.48 89.91 20.07 4.48 1 2.799424 0.079198 2.761108 1.3739864.5 91.12 20.25 4.5 1 2.875 0.078177 2.837212 1.393650

4.52 92.34 20.43 4.52 1 2.949376 0.077018 2.912188 1.4092634.54 93.57 20.61 4.54 1 3.022408 0.075721 2.985892 1.4205954.56 94.81 20.79 4.56 1 3.093952 0.074286 3.05818 1.4274314.58 96.07 20.97 4.58 1 3.163864 0.072716 3.128908 1.4295704.6 97.33 21.16 4.6 1 3.232 0.071010 3.197932 1.426831

4.62 98.61 21.34 4.62 1 3.298216 0.069170 3.265108 1.4190524.64 99.89 21.52 4.64 1 3.362368 0.067197 3.330292 1.4060934.66 101.1 21.71 4.66 1 3.424312 0.065092 3.39334 1.3878404.68 102.5 21.90 4.68 1 3.483904 0.062858 3.454108 1.3642084.7 103.8 22.09 4.7 1 3.541 0.060497 3.512452 1.335143

4.72 105.1 22.27 4.72 1 3.595456 0.058012 3.568228 1.3006314.74 106.4 22.46 4.74 1 3.647128 0.055407 3.621292 1.2607014.76 107.8 22.65 4.76 1 3.695872 0.052687 3.6715 1.2154334.78 109.2 22.84 4.78 1 3.741544 0.049859 3.718708 1.1649744.8 110.5 23.04 4.8 1 3.784 0.046930 3.762772 1.109550

4.82 111.9 23.23 4.82 1 3.823096 0.043914 3.803548 1.0494894.84 113.3 23. 42 4. 84 1 3.858688 0.040826 3.840892 0.9852634.86 114.7 23.61 4.86 1 3.890632 0.037668 3.87466 0.917533

4.88 116.2 23.81 4.88 1 3.918784 0.034533 3.904708 0.8472354.9 117.6 24.01 4.9 1 3.943 0.031407 3.930892 0.775712

4.92 119.0 24.20 4.92 1 3.963136 0. 028380 3.953068 0. 7049134.94 120.5 24.40 4.94 1 3.979048 0.025557 3.971092 0. 6376904.96 122.0 24.60 4.96 1 3.990592 0.023092 3.98482 0.5781754.98 123.5 24.80 4.98 1 3.997624 0.021200 3.994108 0.532034

5 125 25 5 1 4 0.).20140 3.998812 0.506039

TOTAL: 51.21251

-BlO-

a b c d 5 TO 6SUB- 3 -51 285 -521 -

STATION AVG SURFNUMBER: x^3 x^2 xAl xÔ U(x) L(i) RADIUS AREA

5 125 25 5 1 45.02 126.5 25.20 5.02 1 3.997624 0.020140 3.998812 0.5060395.04 128.0 25.40 5.04 1 3.990592 0.021200 3.994108 0.5320345.06 129.5 25.60 5.06 1 3.979048 0.023092 3.98482 0.5781755.08 131.0 25.80 5.08 1 3.963136 0.025557 3.971092 0.6376905.1 132.6 26.01 5.1 1 3.943 0.028380 3.953068 0.7049135.12 134.2 26.21 5.12 1 3.918784 0.031407 3.930892 0.7757125.14 135.7 26.41 5.14 1 3.890632 0.034533 3.904708 0.8472355.16 137.3 26.62 5.16 1 3.858688 0.037688 3.87466 0.9175335.18 138.9 26.83 5.18 1 3.823096 0.040826 3.840892 0.9852635.2 140.6 27.04 5.2 1 3.784 0.043914 3.803548 1.0494895.22 142.2 27.24 5.22 1 3.741544 0.046930 3.762772 1.1095505.24 143.8 27.45 5.24 1 3.695872 0.049859 3.718708 1.1649745.26 145.5 27.66 5.26 1 3.647128 0.052687 3.6715 1.2154335.20 147.1 27.87 5.28 1 3.595456 o.055407 3.621292 1.2607015.3 148.8 28.09 5.3 1 3.541 0.058012 3.568228 1.300631

5.32 150.5 28.30 5.32 1 3.483904 0.060497 3.512452 1.3351435.34 152.2 28.51 5.34 1 3.424312 0.062858 3.454108 1.3642085.36 153.9 28.72 5.36 1 3.362368 0.065092 3.39334 1.3878405.38 155.7 28.94 5.38 1 3.298216 0.067197 3.330292 1.4060935.4 157.4 29.16 5.4 1 3.232 0.069170 3.265108 1.419052

5.42 159.2 29.37 5.42 1 3.163864 0.071010 3.197932 1.4268315.44 160.9 29.59 5.44 1 3.093952 0.072716 3.128908 1.4295705.46 162.7 29.81 5.46 1 3.022408 0.074286 3.05818 1.4274315.48 164.5 30.03 5.48 1 2.949376 0.075721 2.985892 1.4205955.5 166.3 30.25 5.5 1 2.875 0.077018 2.912188 1.409263

5.52 168.1 30.47 5.52 1 2.799424 0.078177 2.837212 1.3936505.54 170.0 30.69 5.54 1 2.722792 0.079198 2.761108 1.3739865.56 171.8 30.91 5.56 1 2.645248 0.080081 2.68402 1.3505125.58 173.7 31.13 5.58 1 2.566936 0.080825 2.606092 1.3234825.6 175.6 31.36 5.6 1 2.488 0.081430 2.527468 1.293157

5.62 177.5 31.58 5.62 1 2.408584 0.081895 2.448292 1.2598075.64 179.4 31.80 5.64 1 2.328832 0.082221 2.368708 1.2237055.66 181.3 32.03 5.66 1 2.248888 0.082407 2.28886 1.1851335.68 183.2 32.26 5.68 1 2.168896 0.082454 2.208892 1.1443735.7 185.1 32.49 5.7 1 2.089 0.082361 2.128948 1.1017115.72 187.1 32.71 5.72 1 2.009344 0.082128 2.049172 1.0574305.74 189.1 32.94 5.74 1 1.930072 0.081756 1.969708 1.0118165.76 191.1 33.17 5.76 1 1.851328 0.081244 1.8907 0.9651495.78 193.1 33.40 5.78 1 1.773256 0.080593 1.812292 0.9177105.8 195.1 33.64 5.8 1 1.696 0.079802 1.734628 0.8697705.82 197.1 33.87 5.82 1 1.619704 0.078873 1.657852 0.8215965.84 199.1 34.10 5.84 1 1.544512 0.077806 1.582108 0.7734485.86 201.2 34.33 5.86 1 1.470568 0.076601 1.50754 C).7255765.88 203.2 34.57 5.88 1 1.398016 0.075258 1.434292 0.6762205.9 205.3 34.81 5.9 1 1.327 0.073776 .362508 0.631609

5.92 207.4 35.04 5.92 1 1.257664 0. 072162 1.292332 0.5859595.94 209.5 35.28 5.94 1 1. 190152 0.070412 1.'223908 0.5414725.96 211.7 35.52 5.96 1 1.124608 0.068527 1.15738 0.4983345.98 213.8 35.76 5.98 1 1.061176 0.066510 1.0'28922 0.456715

6 216 36 6 I 1 0.064362 1.030588 0.416769

TOTAL: 51.21251

a b c d 6 TO 7SUB- -1 21 -147 343STATION AVG SURFNUMBER: x"3 x"2 x~l x"O U(x) L(i) RADIUS AREA

6 216 36 6 1 16.02 218.1 36.24 6.02 1 0.941192 0.062115 0.970596 0.3788096.04 220.3 36.48 6.04 1 0.884736 0.059893 0.912964 0.3435706.06 222.5 36.72 6.06 1 0.830584 0.057727 0.85766 0.3110826.08 224.7 36.96 6.08 1 0.778688 0.055616 0.804636 0.2811796.1 226.9 37.21 6.1 1 0.729 0.053562 0.753844 0.253699

6.12 229.2 37.45 6.12 1 0.681472 0.051564 0.705236 0.2284896.14 231.4 37.69 6.14 1 0.636056 0.049624 0.658764 0.2054036.16 233.7 37.94 6.16 1 0.592704 0.047743 0.61438 0.184300

6.18 236.0 38.19 6.18 1 0.551368 0.045920 0.572036 0.1650466.2 238.3 38.44 6.2 1 0.512 0.044156 0.531684 0.147513

6.22 240.6 38.68 6.22 1 0.474552 0.042454 0.493276 0.1315796.24 242.9 38.93 6.24 1 0.438976 0.040812 0.456764 0.1171286.26 245.3 39.18 6.26 1 0.405224 0.039232 0.4221 0.1040506.28 247.6 39.43 6.28 1 0.373248 0.037715 0.389236 0.0922386.3 250.0 39.69 6.3 1 0.343 0.036262 0.358124 0.0815956.32 252.4 39.94 6.32 1 0.314432 0.034873 0.328716 0.0720266.34 254.8 40.19 6.34 1 0.287496 0.033549 0.300964 0.0634416.36 257.2 40.44 6.36 1 0.262144 0.032291 0.27482 0.0557586.38 259.6 40.70 6.38 1 0.238328 0.031099 0.250236 0.0488976.4 262.1 40.96 6.4 1 0.216 0.029975 0.227164 0.042784

6.42 264.6 41.21 6.42 1 0.195112 0.028918 0.205556 0.0373506.44 267.0 41.47 6.44 1 0.175616 0.027930 0.185364 0.0325296.46 269.5 41.73 6.46 1 0.157464 0.027009 0.16654 0.0282626.48 272.0 41.99 6.48 1 0.140608 0.026155 0.149036 0.0244926.5 274.6 42.25 6.5 1 0.125 0.025369 0.132804 0.0211696.52 277.1 42.51 6.52 1 0.110592 0.024649 0.117796 0.0182436.54 279.7 42.77 6.54 1 0.097336 0.023994 0.103964 0.0156736.56 282.3 43.03 6.56 1 0.085184 0.023402 0.09126 0.0134196.58 284.8 43.29 6.58 1 0.074088 0.022871 0.079636 0.0114446.6 287.4 43.56 6.6 1 0.064 0.022400 0.069044 0.0097176.62 290.1 43.82 6.62 1 0.054872 0.021984 0.059436 0.0082106.64 292.7 44.08 6.64 1 0.046656 0.021621 0.050764 0.0068966.66 295.4 44.35 6.66 1 0.039304 0.021308 0.04298 0.0057546.68 298.0 44.62 6.68 1 0.032768 0.021040 0.036036 0.0047646.7 300.7 44.89 6.7 1 0.027 0.020815 0.029884 0.003908

6.72 303.4 45.15 6.72 1 0.021952 0.020627 0.024476 0.0031726.74 306.1 45.42 6.74 1 0.017576 0.020473 0.019764 0.0025426.76 308.9 45.69 6.76 1 0.013824 0.020348 0.0157 0.0020076.78 311.6 45.96 6.78 1 0.010648 0.020250 0.012236 0.0015566.8 314.4 46.24 6.8 1 0.008 0.020174 ).009324 0.0011816.82 317.2 46.51 6.82 1 0.005832 0.020117 0.006916 0.0008746.84 320.0 46.78 6.84 1 0.004096 0.020075 0.004964 0.0006266.86 322.8 47.05 6.86 1 0.002744 0.020045 0. 00342 0. 0004306.88 325.6 47.33 6.88 1 0. 001728 0.020025 0.002236 0.0002816.9 328.5 47.61 6.9 1 0.001 C). 020013 0. 001364 0. 000171

6.92 331.3 47.88 6.92 1 0. |000512 0. 020005 0. 000756 0. 000C)c)56.94 334.2 48. 16 6.94 1 0.000216 0.020002 0.000364 0.(000456.96 337.1 48.44 6.96 1 0. 000064 0. 02000C) 0. 0C) 14 0. C)00C) 176.9 340 . 0 48.72 6.98 1 0. 000008 0.020000 0.('00036 0. 000Ci0O4

7 343 49 7 1 9. 4E-14 0. 020000 0.')000004 0.0000

TOTAL: 3.563441

-B12-

a b c d 7 TO 8SUB- ************************STATION AVG SURFNUMBER: x^3 x^2 x^l x"O U(x) L(i) RADIUS AREA

7 343 49 7 1 07.02 345.9 49.28 7.02 1 2.2E-18 0.02 1.IE-18 1.4E-197.04 348.9 49.56 7.04 1 4.2E-18 0.02 3.2E-18 4.1E-197.06 351.8 49.84 7.06 1 6.OE-18 0.02 5.1E-18 6.4E-197.08 354.8 50.12 7.08 1 7.6E-18 0.02 6.BE-18 8.5E-197.1 357.9 50.41 7.1 1 8.9E-18 0.02 8.3E-18 1.OE-18

7.12 360.9 50.69 7.12 1 1.OE-17 0.02 9.5E-18 1.2E-187.14 363.9 50.97 7.14 1 1.1E-17 0.02 1.1E-17 1.3E-187.16 367.0 51.26 7.16 1 1.2E-17 0.02 1.2E-17 1.4E-187.18 370.1 51.55 7.18 1 1.3E-17 0.02 1.2E-17 1.5E-187.2 373.2 51.84 7.2 1 1.3E-17 0.02 1.3E-17 1.6E-18

7.22 376.3 52.12 7.22 1 1.3E-17 0.0' 1.3E-17 1.7E-187.24 379.5 -2.41 7.24 1 1.4E-17 0.02 1.3E-17 1.7E-187.26 382.6 52.70 7.26 1 1.4E-17 0.02 1.4E-17 1.7E-187.28 385.8 52.99 7.28 1 1.4E-17 0.02 1.4E-17 1.7E-187.3 389.0 53.29 7.3 1 1.3E-17 0.02 1.3E-17 1.7E-18

7.32 392.2 53.56 7.32 1 1.3E-17 0.02 1.3E-17 1.7E-187.34 395.4 53.87 7.34 1 1.3E-17 0.02 1.3E-17 1.6E-187.36 398.6 54.16 7.36 1 1.2E-17 0.02 1.2E-17 1.6E-187.38 401.9 54.46 7.38 1 1.2E-17 0.02 1.2E-17 1.5E-187.4 405.2 54.76 7.4 1 1.1E-17 0.02 1.1E-17 1.4E-18

7.42 408.5 55.05 7.42 1 1.OE-17 0.02 1.1E-17 1.3E-187.44 411.8 55.35 7.44 1 9.6E-18 0.02 1.OE-17 1.3E-187.46 415.1 55.65 7.46 1 8.8E-18 0.02 9.2E-18 1.2E-187.48 418.5 55.95 7.48 1 7.9E-18 0.02 8.4E-18 1.OE-187.5 421.8 56.25 7.5 1 7.1E-18 0.02 7.5E-18 9.4E-197.52 425.2 56.55 7.52 1 6.2E-18 0.02 6.6E-18 8.3E-197.54 428.6 56.85 7.54 1 5.2E-18 0.02 5.7E-18 7.2E-197.56 432.0 57.15 7.56 1 4.3E-18 0.02 4.8E-18 6.OE-197.58 435.5 57.45 7.58 1 3.4E-18 0.02 3.9E-18 4.9E-197.6 438.9 57.76 7.6 1 2.5E-18 0.02 3.OE-18 3.7E-19

7.62 442.4 58.06 7.62 1 1.6E-18 0.02 2.1E-18 2.6E-197.64 445.9 58.36 7.64 1 7.7E-19 0.02 1.2E-18 1.5E-197.66 449.4 58.67 7.66 1 -5.OE-20 0.02 3.6E-19 4.5E-207.68 452.9 58.98 7.68 1 -8.2E-19 0.02 4.4E-19 5.5E-207.7 456.5 59.29 7.7 1 -1.5E-18 0.02 1.2E-18 1.5E-19

7.72 460.0 59.59 7.72 1 -2.2E-18 0.02 1.9E-18 2.3E-197.74 463.6 59.90 7.74 1 -2.8E-18 0.02 2.5E-18 3.1E-197.76 467.2 60.21 7.76 1 -3.3E-18 0.02 3.OE-18 3.8E-197.78 470.9 60.52 7.78 1 -3.7E-18 0.02 3.5E-18 4.4E-197.0 474.5 60.84 7.8 1 4. E 18 ('.C 3.9E-18 4.8E-197.82 478.2 61.15 7.82 1 -4.2E-18 0.02 4.1E-18 5.E- 191.84 481.8 61.46 7.84 1 -4.3E-18 ().02 4.3E-18 5.4E-197.86 485.5 61.77 7.86 1 -4.3E-18 0.02 4.3E-13 5.4E-197.88 489.3 62.09 7.88 1 -4.2E- 18 (). 02 4.2E- 18 5.3E- 197.9 493.0 62.41 7.9 1 -3.9E-18 0.02 4.0E-18 5. CE-19

7.92 496.7 62.72 7.92 1 -3.4E-18 0.0'Z 3.6E-18 4. 6E- 197.94 500.5 63.04 7.94 1 -2.8E- 18 0'. 02 3-. 1 E- 18 3.9E- 197.96 504.3 63.36 7.96 i -2.1 E- 18 0. 02 2.4E-18 3. 1 E 197.98 508.1 63.68 7.98 1 -1.1E-18 C.02 1.6E-18 :.CE-19

a 512 64 8 1 C) 0.02 5.6E-19 .,E-2C)

TOTAL: 4.2E-17

- - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ---- -

a b c d 8 TO 9SU B- --- --- --- --- --- --- --- - -

STATION AVG SURFNUMBER: x^3 x^2 x'1 xÔ U(x) Lu:) RADIUS AREA

8 512 64 8 1 08.02 515.8 64.32 8.02 1 1.2E-18 0.02 5.9E-19 7.4E-208.04 519.7 64.64 8.04 1 2.3E-18 0.02 1.7E-18 2.2E-198.06 523.6 64.96 8.06 1 3.3E-18 0.02 2.8E-18 3.5E-198.08 527.5 65.28 8.08 1 4.2E-18 0.02 3.7E-18 4.7E-198.1 531.4 65.61 8.1 1 5.1E-18 0.02 4.6E-18 5.8E-19

8.12 535.3 65.93 8.12 1 5.9E-18 0.02 5.5E-18 6.9E-198.14 539.3 66.25 8.14 1 6.6E-18 0.02 6.2E-18 7.8E-198.16 543.3 66.58 8.16 1 7.2E-18 0.02 6.9E-18 8.7E-198.18 547.3 66.91 8.18 1 7.8E-18 0.02 7.5E-18 9.5E-198.2 551.3 67.24 8.2 1 8.4E-18 0.02 8.1E-18 1.OE-188.22 555.4 67.56 8.22 1 8.8E-18 0.02 8.6E-18 1.E-188.24 559.4 67.89 8.24 1 9.2E-18 0.02 9.OE-18 i.IE-188.26 563.5 68.22 8.26 1 9.6E-18 0.02 9.4E-18 1.2E-188.28 567.6 68.55 8.28 1 9.9E-18 0.02 9.7E-18 1.2E-188.3 571.7 68.89 8.3 1 1.OE-17 0.02 1.OE-17 1.3E-18

8.32 575.9 69.22 8.32 1 1.OE-17 0.02 1.OE-17 1.3E-188.34 580.0 69.55 8.34 1 1.OE-17 0 .02 1.OE-17 1.3E-188.36 584.2 69.88 8.36 1 1.OE-17 0.02 I.OE-17 1.3E-188.38 588.4 70.22 8.38 1 1.1E-17 0.02 1.1E-17 1.3E-188.4 592.7 70.56 8.4 1 1.1E-17 0.02 1.1E-17 1.3E-18

8.42 596.9 70.89 8.42 1 I.OE-17 0.02 1.OE-17 1.3E-188.44 601.2 71.23 8.44 1 1.OE-17 0.02 1.OE-17 1.3E-188.46 605.4 71.57 8.46 1 1.OE-17 0.02 1.OE-17 1.3E-188.48 609.8 71.91 8.48 1 1.OE-17 0.02 1.OE-17 1.3E-188.5 614.1 72.25 8.5 1 9.9E-18 0.02 1.OE-17 1.3E-188.52 618.4 72.59 8.52 1 9.7E-18 0.02 9.8E-18 1.2E-188.54 622.8 72.93 8.54 1 9.4E-18 0.02 9.5E-18 1.2E-188.56 627.2 73.27 8.56 1 9.1E-18 0.02 9.3E-18 1.2E-188.58 631.6 73.61 8.58 1 8.8E-18 0.02 9.OE-18 1.1E-188.6 636.0 73.96 8.6 1 8.5E-18 0.02 8.7E-18 1.1E-18

8.62 640.5 74.30 8.62 1 8.1E-18 0.02 8.3E-18 1.OE-188.64 644.9 74.64 8.64 1 7.8E-18 0.02 8.OE-18 1.OE-188.66 649.4 74.99 8.66 1 7.4E-18 0.02 7.6E-18 9.5E-198.68 653.9 75.34 8.68 1 7.OE-18 0.02 7.2E-18 9.OE-198.7 658.5 75.69 8.7 1 6.5E-18 0.02 6.8E-18 8.5E-19

8.72 663.0 76.03 8.72 1 6.1E-18 0.02 6.3E-18 8.OE-198.74 667.6 76.38 8.74 1 5.7E-18 0. 0'2 5.9E-18 7.4E-198.76 672.2 76.73 8.76 1 5.2E-18 0.02 5.4E-18 6.8E-198.78 676.8 77.08 8.78 1 4.BE-18 0.02 5.OE-18 6.3E-198.8 681.4 77.44 8.8 1 4.3E-18 0.02 4.5E-18 5.7E-19

8.82 686.1 77.79 8.82 1 3.9E-18 0.02 4. E-18 5. 1E-198.84 690.8 78.14 8.84 1 3.4E-18 0. 02 3.6E-18 4.6E-198.86 695.5 78.49 8.86 1 2.9E-18 ('.02 3.2E-18 4.0E-198.88 700.2 78.85 8.88 1 2.5E-18 0.02 2.7E-10 3.4E-198.9 704.9 79.21 8.9 1 2.OE-18 0. )2 2.3E-18 2.9E-19

8.92 709.7 79.56 8.92 1 i.6E-18 ( 02 1.BE-18 2.3E-198.94 714.5 79.92 8.94 1 1.2E-18 0.02 1.4E-18 1.3E-198.96 719.2 80.28 8.96 1 7.BE-19 0.02 9.8E-1i 1.2E-198.98 724.1 30.64 8.98 1 3.8E-19 0.02 5.8E-19 7.3E-20

9 729 81 9 1 0 0.02 1.9E-19 2.4E-20

TOTAL: 4.E-17

-B14-

a b d 9 TO 10S U B - -----------------------------. .- -

STATION AVG SURFNUMBER: x^3 x'2 x^l x'O U(x) L(i) RADIUS AREA

9 729 81 9 1 09.02 733.8 81.36 9.02 1 -3.6E-19 0.02 1.BE-19 2.3E-209.04 738.7 81.72 9.04 1 -7.OE-19 0.02 5.3E-19 6.6E-209.06 743.6 82.08 9.06 1 -1.OE-18 0.02 8.6E-19 1.1E-199.08 748.6 82.44 9.08 1 -1.3E-18 0.02 1.2E-18 1.5E-199.1 753.5 82.81 9.1 1 -1.6E-18 0.02 1.4E-18 1.8E-199.12 758.5 83.17 9.12 1 -1.8E-18 0.02 1.7E-18 2.2E-199.14 763.5 83.53 9.14 1 -2.1E-18 0.02 2.OE-18 2.5E-199.16 768.5 83.90 9.16 1 -2.3E-18 0.02 2.2E-18 2.7E-199.18 773.6 84.27 9.18 1 -2.5E-18 0.02 2.4E-18 3.OE-199.2 778.6 84.64 9.2 1 -2.7E-18 0.02 2.6E-18 3.2E-19

9.22 783.7 85.00 9.22 1 -2.8E-18 0.02 2.8E-18 3.5E-199.24 788.8 85.37 9.24 1 -3.OE-18 0.02 2.9E-18 3.6E-199.26 794.0 85.74 9.26 1 -3.1E-18 0.02 3.0E-18 3.8E-199.28 799.1 86.11 9.28 1 -3.2E-18 0.02 3.2E-18 4.0E-193.3 804.3 86.49 9.3 1 -3.3E-18 0.2 3 .3E-18 4. 1E-19

9.32 809.5 86.86 9.32 1 -3.4E-18 0.02 3.3E-18 4.2E-199.34 814.7 87.23 9.34 1 -3.5E-18 0.02 3.4E-18 4.3E-199.36 620.0 87.60 9.36 1 -3.5E-18 0.02 3.5E-18 4.4E-199.38 825.2 87.98 9.38 1 -3.5E-18 0.02 3.5E-18 4.4E-199.4 830.5 88.36 9.4 1 -3.6E-18 0.02 3.5E-18 4.5E-19

9.42 835.8 88.73 9.42 1 -3.6E-18 0.02 3.6E-18 4.5E-199.44 841.2 89.11 9.44 1 -3.6E-18 0.02 3.6E-18 4.5E-199.46 846.5 89.49 9.46 1 -3.5E-18 0.02 3.6E-18 4.5E-199.48 851.9 89.87 9.48 1 -3.5E-18 0.02 3.5E-18 4.4E-199.5 857.3 90.25 9.5 1 -3.5E-18 0.02 3.5E-18 4.4E-199.52 862.8 90.63 9.52 1 -3.4E-18 0.02 3.5E-18 4.3E-199.54 868.2 91.01 9.54 1 -3.4E-18 0.02 3.4E-18 4.3E-199.56 873.7 91.39 9.56 1 -3.3E-18 0.02 3.3E-18 4.2E-199.58 879.2 91.77 9.58 1 -3.2E-18 0.02 3.2E-18 4.1E-199.6 884.7 92.16 9.6 1 -3.1E-18 0.02 3.2E-18 4.OE-19

9.62 890.2 92.54 9.62 1 -3.0E-18 0.02 3.1E-18 3.9E-199.64 895.8 92.92 9.64 1 -2.9E-18 ).02 3.0E-18 3.7E-199.66 901.4 93.31 9.66 1 -2.8E--18 0.02 2.8E-18 3.6E-199.68 907.0 93.7: 9.68 1 -2.7E- 18 0.02 '. 7E- 18 3.4E-199.7 912.6 94. 09 9.7 1 -2.5E-18 0.02 Z. 6E- 18 3.3E- 19

9.72 918.3 94.47 9.72 1 -2.4E-18 0.0)2 2'.5E-18 3.1E-199.74 924.0 94.86 9.74 1 -2.2E- 18 0 .02 2.3E-18 2.9E-199.76 929.7 95.25 9.76 1 -2.1E-18 0.02 2.2E-18 2.7E-199.78 935.4 95.64 9.78 1 -1.9E-18 ).02 2.0E-18 2.5E-199.8 941.1 96.04 9.8 1 -1.8E-18 0.n2 1.9E-18 2.3E-193.82 946.9 96.43 9.82 1 -1.6E-18 .02 1.7E-18 2. 1E-199.84 952.7 96.82 9.84 1 -1.4E-18 C.2 1.5E-18 1.9E-193.86 958.5 97.21 9.86 1 -1.3E-18 0 1.4E--18 1.7E-199.88 964.4 97.61 9.88 1 -1. 1E-18 C).02 1.2E-18 1.5E-199.9 970.2 98.01 9.9 1 -9. 2E-19 2C) .E-18 1.3E-19

9. 02 976.1 98.40 9.92 1 -7.4E-19 0.0 C .3E-19 1.0E-199.94 982.1 98.80 9.34 1 -5.5E-19 .2 G .5E-19 8. 1E-209.96 986. C) '39.20 9.96 1 -3.7E-19 C 02 4. 6E-19 5. 6E-209.98 994.0 99.60 9.98 1 --1.'3E-19 o. 02 2.8E-1 3.5E-20-

10 10C0C) 110 1C 1 C) 0. 2 .3E-20 1.2E-20

-DTAL: 1.5E- 17

-B15-

"HERMFAST.WK1" USED TO F IND THE INTERPOLATING POLYNOMIALS AND SURFACE

AREA OF A BODY OF REVOLUTION.

The inputs are the station radii and slopes, and interstation distances.The outputs are cubic polynomials which describe the radius of the bodybetween stations, and are used to calculate the body surface area.The generated polynomials and their first derivatives are CONTINUOUSover the length of the body, which is ideal for submarine surface areacalculation.

CAUTION: IF THE ACTUAL INPUT BODY HAS DISCONTINUOUS FIRST DERIVATIVES,THE LOCATION OF THE SLOPE DISCONTINUITY SHOULD BE TREATED AS TWOVERY CLOSE STATIONS, EACH WITH ITS OWN SLOPE!

PROCEDURE:(1) INPUT ACTUAL RADII, SLOPES, AND STATION SPACINGS.(2) HIT EF9] TO CALCULATE INTERPOLATING COEFFICIENTS, AND AREAS.

INPUTS: OUTPUT

ACTUAL ACTUAL ACTUAL ACTUALINTER- INTERVAL STATION STATION SURFACEVAL LENGTH: STATION RADIUS: SLOPE: AREA INTERVA

0: 0 6 J0 TO 1 2 1: 4.21 1.3 . 6S.62719 0 TO I1 TO 2 3.92 2: 7.78 0.9 K 202.5642 1 TO 22 TO 3 11.78 3: 12.01 0.01 . 858.7818 2 TO 33 TO 4 11.05 4: 12.5 0 S 852.4521 3 TO 44 TO 5 101.18 5: 12.5 0 . 7946.658 4 TO 55 TO 6 26.5 6: 11.95 -0.02 2043.290 5 TO 66 TO 7 24.81 7: 10.23 -0.09 1 1755.597 6 TO 77 TO 8 25.94 8: 6.48 -0.13 9 1389.976 7 TO 88 TO 9 23 9: 0 -0.25 8 519.0502 8 TO 99 TO 10 0.001 10: 0 0 8 0.000000 9 TO 10

230.181 18078.373 12.5 15636.99 TOTALTOTAL CYLYNDER MAX =+=+=+=+=+

LENGTH SURFACE RADIUS TYPE 2400 588 other

AREA =+=+=+=+=+

16224.99 GRAND

RELATIONS:LET lamda = 1THEN: X = l*xAND: U(X) = l*U(x)

SO: A = a/1AND: B = b/1AND: C: = .:AND: D = d*l

-B16-

AUXILIARY OUTPUT

OUTPUT: COEFF. OF (ACTUAL) INTERPOLATING POLYNOMIALS, U(X).A B C D

0 to 1: 7.73E-01 -3.49E+00 6.00E+00 O.OOE+001 to 2: 2.46E-02 -4.86E-01 3.97E+00 -5.38E+002 to 3: 1.38E-03 -1.60E-01 6.13E+00 -6.60E+013 to 4: -6.44E-04 7.43E-02 -2.79E+00 4.64E+014 to 5: O.OOE+00 O.OOE+O0 O.OOE+00 1.25E+015 to 6: 3.06E-05 -1.38E-02 2.04E+00 -8.68E+016 to 7: 4.66E-05 -2.39E-02 4.01E+00 -2.08E+027 to 8: 1.03E-04 -6.07E-02 1.18E+01 -7.46E+028 to 9: 3.47E-04 -2.06E-01 4.05E+01 -2.62E+039 - 10: -2.50E+05 7.25E+03 -7.00E+01 2.25E-01

(ACTUAL -- > "X") X-3 X^2 X 1

AUXILIARY OUTPUT

OUTPUT: COEFF. OF (NORMAL) INTERPOLATING POLYNOMIALS, U(x).a b c d

0 to 1: 3.09 -6.985 6 01 to 2: 0.3785714 -1.903571 3.9714285 -1.3724482 to 3: 0.1918336 -1.883752 6.1330050 -5.6052293 to 4: -0.078687 0.8212217 -2.792760 4.19873304 to 5: 0 0 0 0.12354225 to 6: 0.0215094 -0.364905 2.0358490 -3.2735846 to 7: 0.0286537 -0.593748 4.0103748 -8.3948567 to 8: 0.0691287 -1.575397 11.803631 -28.747758 to 9: 0.1834782 -4.738695 40.461304 -114.07309 - 10: -0.25 7.25 -70 225

(NORMAL -- > "x") x^3 x^2 x I

INTERMEDIATE OUTPUT

L NRMLIZD NRMLIZDSTATION SURF

INTERVAL STATION RADIUS: INTERVAL AREA

0 TO 1: 0: 01: 2.105 0 TO 1 17.15

1 TO 2: 1: 1.073979 1 TO 2 13.182: 1.984693 2 TO 3 6.188

2 TO 3 2: 0.660441 3 TO 4 6.9813: 1.019524 4 TO 5 0.776

3 TO 4 3: 1.086877 5 TO 6 2.9094: 1.131221 6 TO 7 2.852

4 TO 5 4: 0.123542 7 TO 8 2.0655: 0.123542 8 TO 9 0.981

5 TO 6 5: 0.471698 9 TO 10 0.1296: 0.450943

6 TO 7 6: 0.481660 53.227: 0.412333

7 TO 8 7: 0.394371 TOTAL8: 0.249807 NRMLIZD8: 0.281739 AREA9: 09: 0

10: 0

-B18-

0 TO 1: matrix input: IF]

XO: 0 0 0 0 1XI: 1 [F]= 1 1 1 1

0 0 1 0LOCAL INPUTS: 3 2 1 0UO: 0

Ul: 2.105 DET [F] = -1SO: 6Si: 1.3 2 -2 1 1

EUS] [F]'-I -3 3 -2 -1LOCAL COEFFICIENTS: 0 0 1 0a: 3.09 1 0 0 0b: -6.98c: 6d : 0

CC]

SUB- a b c d 0 TO ISTATION 3.09 -6.98 6 0-------------------------------------NUMBER: ------------------------ AVG SURF"x" X^3 x'^2 x^l xÔ U(x) L(i) RADIUS AREA

0 0 0 0 1 00.1 0.001 0.01 0.1 1 0.53324 0.542535 0.26662 0.9088680.2 0.008 0.04 0.2 1 0.94532 0.424040 0.73928 1.9696790.3 0.027 0.09 0.3 1 1.25478 0.325216 1.10005 2.2478340.4 0.064 0.16 0.4 1 1.48016 0.246568 1.36747 2.1185350.5 0.125 0.25 0.5 1 1.64 0.188543 1.56008 1.8481590.6 0.216 0.36 0.6 1 1.75284 0.150774 1.69642 1.6070900.7 0.343 0.49 0.7 1 1.83722 0.130843 1.79503 1.4757170.8 0.512 0.64 0.8 1 1.91168 0.124676 1.87445 1.4683820.9 0.729 0.81 0.9 1 1.99476 0.130008 1.95322 1.595525

1 1 1 1 1 2.105 0.148838 2.04988 1.917004

TOTAL: 17.15679

-B19-

1 TO 2: matrix input: [F]

XI: 1 1 1 1 1X2: 2 EF]= 8 4 2 1

3 2 1 0LOCAL INPUTS: 12 4 1 0UI: 1.073

U2: 1.984 DET IF] = -1Si: 1.3S2: 0.9 2 -2 1 1

EF] -I -9 9 -5 -4LOCAL COEFFICIENTS: 12 -12 8 5a: 0.378 -4 5 -4 -2b: -1.90c: 3.971d: -1.37

SUB- a b c d 1 TO 2STATION 0.378 -1.90 3.971 -1.37- ------------------------------------NUMBER: AVG SURF"x" x^3 x^2 xA1 x"O U(x) L(i) RADIUS AREA

1 1 1 1 1 1.0739791.1 1.331 1.21 1.1 1 1.196679 0.158288 1.135329 1.1291491.2 1.728 1.44 1.2 1 1.306293 0.148375 1.251486 1.1667241.3 2.197 1.69 1.3 1 1.405093 0.140575 1.355693 1.1974311.4 2.744 1.96 1.4 1 1.495351 0.134708 1.450222 1.2274651.5 3.375 2.25 1.5 1 1.579336 0.130589 1.537343 1.2614171.6 4.096 2.56 1.6 1 1.659322 0.128053 1.619329 1.3028871.7 4.913 2.89 1.7 1 1.737579 0.126981 1.698451 1.3551011.8 5.832 3.24 1.8 1 1.816379 0.127316 1.776979 1.4214981.9 6.859 3.61 1.9 1 1.897993 0.129077 1.857186 1.506206

2 8 4 2 1 1.984693 0.132351 1.941343 1.614398

TOTAL: 13.18228

-B20-

2 TO 3: matrix input: [F] (local)

X2: 2 8 4 2 1X3: 3 tF]= 27 9 3 1

12 4 1 0LOCAL INPUTS: 27 6 1 0U2: 0.660

U3: 1.019 DET [F] = -1S2: 0.9S3: 0.01 2 2 1 1

rF]^-1 -15 15 -8 -7LOCAL COEFFICIENTS: 36 -36 21 16a: 0.191 -27 28 -18 -12b: -1.88c: 6.133d: -5.60

SUB- a b c d 2 TO 3STATION 0.191 -1.88 6.133 -5.60-------------------------------------NUMBER: AVG SURFfx" x^3 x^2 x^l xÔ U(x) L(i) RADIUS AREA

2 8 4 2 1 0.6604412.1 9.261 4.41 2.1 1 0.743305 0.129871 0.701873 0.5727312.2 10.64 4.84 2.2 1 0.812666 0.121699 0.777985 0.5948962.3 12.16 5.29 2.3 1 0.869673 0.115107 0.841169 0.6083712.4 13.82 5.76 2.4 1 0.915478 0.109991 0.892576 0.6168562.5 15.62 6.25 2.5 1 0.951233 0.106199 0.933355 0.6228022.6 17.57 6.76 2.6 1 0.978087 0.103543 0.964660 0.6275882.7 19.68 7.29 2.7 1 0.997192 0.101808 0.987639 0.6317762.8 21.95 7.84 2.8 1 1.009699 0.100779 1.003446 0.6353962.9 24.38 8.41 2.9 1 1.016760 0.100248 1.013230 0.638216

3 27 9 3 1 1.019524 0.100038 1.018142 0.639962

TOTAL: 6.188598

-B21-

3 TO 4: matrix input: [F) (local)

X3: 3 27 9 3 1X4: 4 [F]= 64 16 4 1

27 6 1 0LOCAL INPUTS: 48 8 1 0U3: 1.086

U4: 1.131 DET [F] = -1S3: 0.01S4: 0 2 -2 1 1

EF]^-I -21 21 -11 -10LOCAL COEFFICIENTS: 72 -72 40 33a: -0.07 -80 81 -48 -36b: 0.821c: -2.79

d: 4.198

SUB- a b c d 3 TO 4STATION -0.07 0.821 -2.79 4.198- ------------------------------------NUMBER: AVG SURF"x" x^3 x^2 x^1 xÔ U(x) L(i) RADIUS AREA

3 27 9 3 1 1.0868773.1 29.79 9.61 3.1 1 1.088929 0.100021 1.087903 0.6836933.2 32.76 10.24 3.2 1 1.092769 0.100073 1.090849 0.6859063.3 35.93 10.89 3.3 1 1.097926 0.100132 1.095347 0.6891413.4 39.30 11.56 3.4 1 1.103926 0.100179 1.100926 0.6929763.5 42.87 12.25 3.5 1 1.110299 0.100202 1.107113 0.6970303.6 46.65 12.96 3.6 1 1.116572 0.100196 1.113436 0.7009673.7 50.65 13.69 3.7 1 1.122273 0.100162 1.119423 0.7044963.8 54.87 14.44 3.8 1 1.126929 0.100108 1.124601 0.7073733.9 59.31 15.21 3.9 1 1.130070 0.100049 1.128500 0.709406

4 64 16 4 1 1.131221 0.100006 1.130645 0.710452

TOTAL: 6.981447

-B22-


X4: 4 64 16 4 1X5: 5 [F]= 125 25 5 1

48 8 1 0LOCAL INPUTS: 75 10 1 0U4: 0.123

U5: 0.123 DET [F] = -1S4: 0S5: 0 2 -2 1 1

EF]')-I -27 27 -14 -13LOCAL COEFFICIENTS: 120 -120 65 56a: 0 -175 176 -100 -80b: 0c: 0d: 0.123

---------------------------------------------------------------------SUB- a b c d 4 TO 5STATION 0 0 0 0.123-------------------------------------NUMBER: AVG SURF

"x" x^3 x^2 x.1 x-'O U(x) L(i) RADIUS AREA4 64 16 4 1 0.123542

4.1 68.92 16.81 4.1 1 0.123542 0.1 0.123542 0.0776234.2 74.08 17.64 4.2 1 0.123542 0.1 0.123542 0.0776234.3 79.50 18.49 4.3 1 0.123542 0.1 0.123542 0.0776234.4 85.18 19.36 4.4 1 0.123542 0.1 0.123542 0.0776234.5 91.12 20.25 4.5 1 0.123542 0.1 0.123542 0.0776234.6 97.33 21.16 4.6 1 0.123542 0.1 0.123542 0.0776234.7 103.8 22.09 4.7 1 0.123542 0.1 0.123542 0.0776234.8 110.5 23.04 4.8 1 0.123542 0.1 0.123542 0.0:)776234.9 117.6 24.01 4.9 1 0.123542 0.1 0.123542 0.077623

5 125 25 5 1 0. 123542 0.1 0. 123542 0.077623

TOTAL: 0.776238

-B23-

5 TO 6: matrix input: CF] (local)

X5: 5 125 25 5 1X6: 6 [F]= 216 36 6 1

75 10 1 0LOCAL INPUTS: 108 12 1 0US: 0.471

U6: 0.450 DET EF] = -1S5: 0S6: -0.02 2 -2 1 1

IF] .... 1 -33 33 -17 -16

LOCAL COEFFICIENTS: 180 -180 96 85a: 0.021 -324 325 -180 -150b:* -0.36c: 2.035d: -3.27

SUB- a b c d 5 TO 6STATION 0.021 -0.36 2.035 -3.27-------------------------------------NUMBER: AVG SURF"x" x^3 x^2 x'l xÔ U(x) L(i) RADIUS AREA

5 125 25 5 1 0.4716985.1 132.6 26.01 5.1 1 0.471296 0.100000 0.471497 0.2962535.2 140.6 27.04 5.2 1 0.470179 0.100006 0.470738 0.2957925.3 148.8 28.09 5.3 1 0.468475 0.100014 0.469327 0.2949295.4 157.4 29.16 5.4 1 0.466312 0.100023 0.467393 0.2937405.5 166.3 30.25 5.5 1 0.463820 0.100031 0.465066 0.2923005.6 175.6 31.36 5.6 1 0.461129 0.100036 0.462474 0.2906865.7 185.1 32.49 5.7 1 0.458366 0.100038 0.459747 0.2889785.8 195.1 33.64 5.8 1 0.455661 0.100036 0.457014 0.2872555.9 205.3 34.81 5.9 1 0.453144 0.100031 0.454403 0.2856006 216 36 6 1 0.450943 0.100024 0.452043 0.284096

TOTAL: 2.909633

-B24-

6 TO 7: matrix input: CF] (local)

X6: 6 216 36 6 1X7: 7 IF]= 343 49 7 1

108 12 1 0LOCAL INPUTS: 147 14 1 0U6: 0.481

U7: 0.412 DET [F] = -1S6: -0.02S7: -0.09 2 -2 1 1

[F]^-1 -39 39 -20 -19LOCAL COEFFICIENTS: 252 -252 133 120a: 0.028 -539 540 -294 -252b: -0.59c : 4.010d: -8.39

SUB- a b c d 6 TO 7STATION 0.028 -0.59 4.010 -8.39-------------------------------------NUMBER: AVG SURF

x x^3 x^2 x^1 xAO U(x) L(i) RADIUS AREA6 216 36 6 1 0.481660

6.1 226.9 37.21 6.1 1 0.478909 0.100037 0.480285 0.3018866.2 238.3 38.44 6.2 1 0.474770 0.100085 0.476840 0.2998636.3 250.0 39.69 6.3 1 0.469416 0.100143 0.472093 0.2970496.4 262.1 40.96 6.4 1 0.463017 0.100204 0.466216 0.2935316.5 274.6 42.25 6.5 1 0.455747 0.100263 0.459382 0.2894006.6 287.4 43.56 6.6 1 0.447776 0.100317 0.451761 0.2847506.7 300.7 44.89 6.7 1 0.439278 0.100360 0.443527 0.2796816.8 314.4 46.24 6.8 1 0.430423 0.100391 0.434851 0.2742936.9 328.5 47.61 6.9 1 0.421384 0.100407 0.425904 0.268694

7 343 49 7 1 0.412333 0.100408 0.416859 0.262991

TOTAL: 2.852143

-B25-

7 TO 8: matrix input: IF] (local)

X7: 7 343 49 7 1X8: 8 EF]= 512 64 8 1

147 14 1 )LOCAL INPUTS: 192 16 1 0U7: 0.394

U8: 0.249 DET EF] = -1S7: -0.09$8: -0.13 2 -2 1 1

EF] .... -45 45 -23 -22

LOCAL COEFFICIENTS: 336 -336 176 161a: 0.069 -832 833 -448 -392b: -1.57c: 11.80d: -28.7

SUB- a b c d 7 TO 8STATION 0.069 -1.57 11.80 -28.7- ------------------------------------NUMBER: AVG SURF"x" x^3 x^2 x^1 xÔ U(x) L(i) RADIUS AREA

7 343 49 7 1 0.3943717.1 357.9 50.41 7.1 1 0.384203 0.100515 0.389287 0.2458577.2 373.2 51.84 7.2 1 0.371976 0.100744 0.378090 0.2393307.3 389.0 53.29 7.3 1 0.358105 0.100957 0.365041 0.2315587.4 405.2 54.76 7.4 1 0.343004 0.101133 0.350555 0.2227577.5 421.8 56.25 7.5 1 0.327089 0.101258 0.335047 0.2131657.6 438.9 57.76 7.6 1 0.310773 0.101322 0.318931 0.2030407.7 456.5 59.29 7.7 1 0.294473 0.101319 0.302623 0.1926537.8 474.5 60.84 7.8 1 0.278601 0.101251 0.286537 0.1822907.9 493.0 62.41 7.9 1 0.263575 0.101122 0.271088 0.172242

8 512 64 8 1 0.249807 0.100943 0.256691 0.162805

TOTAL: 2.065701

-B26-


XS: 8 512 64 8 1X9: 9 [F]= 729 81 9 1

192 16 1 0LOCAL INPUTS: 243 18 1 0U8: 0.281

U9: 0 DET [F] -1S8: -0.1369: -0.25 2 -2 1 1

[F]^-I -51 51 -26 -25LOCAL COEFFICIENTS: 432 -432 225 208a: 0.183 -1215 1216 -648 -576b: -4.73c: 40.46d: -114.

SUB- a b c d 8 TO 9STATION 0.183 -4.73 40.46 -114.-- ------------------------------------NUMBER: AVG SURFS"X1" x^3 x^2 x^1 x^0 U(x) L(i) RADIUS AREA

8 512 64 8 1 0.2817398.1 531.4 65.61 8.1 1 0.265570 0.101298 0.273654 0.1741758.2 551.3 67.24 8.2 1 0.243798 0.102342 0.254684 0.1637718.3 571.7 68.89 8.3 1 0.217523 0.103394 0.230660 0.1498478.4 592.7 70.56 8.4 1 0.187846 0.104310 0.202685 0.1328408.5 614.1 72.25 8.5 1 0.155869 0.104988 0.171858 0.1133688.6 636.0 73.96 8.6 1 0.122692 0.105360 0.139280 0.0922038.7 658.5 75.69 8.7 1 0.089415 0.105391 0.106053 0.0702288.8 681.4 77.44 8.8 1 0.057140 0.105079 0.073278 0.0483808.9 704.9 79.21 8.9 1 0.026968 0.104452 0.042054 0.027600

9 729 81 9 1 1.0E-15 0.103572 0.013484 0.008775

TOTAL: 0.981191

-B27-


X9: 9 729 81 9 1X1O: 10 IF]= 1000 100 10 1

243 18 1 0LOCAL INPUTS: 300 20 1 0U9: 0

U1O: 0 DET [F) = -1S9: -0.25S10: 0 2 -2 1 1

[F]"-1 -57 57 -29 -28LOCAL COEFFICIENTS: 540 -540 280 261a: -0.25 -1700 1701 -900 -810b: 7.25C: -70d: 225

SUB- a b c d9 TO 10STATION -0.25 7.25 -70 225-------------------------------------NUMBER: AVG SURF"x" x^3 x^2 x^1 xÔ U(x) L(i) RADIUS AREA

9 729 81 9 1 09.1 753.5 82.81 9.1 1 -0.02025 0.102029 0.010125 0.0064909.2 778.6 84.64 9.2 1 -0.032 0.100687 0.026125 0.0165279.3 804.3 86.49 9.3 1 -0.03675 0.100112 0.034375 0.0216229.4 830.5 88.36 9.4 1 -0.036 0.100002 0.036375 0.0228559.5 857.3 90.25 9.5 1 -0.03125 0.100112 0.033625 0.0211519.6 884.7 92.16 9.6 1 -0.024 0.100262 0.027625 0.0174029.7 912.6 94.09 9.7 1 -0.01575 0.100339 0.019875 0.0125309.8 941.1 96.04 9.8 1 -0.008 0.100299 0.011875 0.0074839.9 970.2 98.01 9.9 1 -0.00225 0.100165 0.005125 0.00322510 1000 100 10 1 0 0.100025 0.001125 0.000707

TOTAL: 0.129997

-Cl1-

APPENDIX C: CALCULATION OF SHAFT HORSEPOWER WHILE SUBMERGED

Essential to the calculation of endurance range and indiscre-tion rate is the calculation of shaft horsepower (SHP) requiredto make a given speed. The following formulas are taken fromReference (16), and is used to determine the required SHP atvarious speeds in submerged operating mode.

SHP - EHP/PC EQN C-1

EHP - 0.00872 (V^3) * [WS*(Cf+Ca+Cr) + (Ss*Cds) + (Sa*Cda)JEQN C-2

where:

SHP - Shaft Horsepower required at the transit speed,operations well-submerged, HP.

EHP - Effective Horsepower, HP.PC - Propulsive Coefficient;

PC assumed to be 0.8.

V - Speed (Submerged), Kts.WS - Wetted Surface Area of Bare Hull, sq ft.Sa - Wetted Surface of Appendages, sq ft.Ss - Wetted Surface of Sail, sq ft.Cf - Coefficient of Frictional Resistance;

Cf - 0.075 / [(logl0(Re#)-2)^2].

Re# - Reynold's Number.Ca - Correlation Allowance;

Ca - 0.0004.

Cr - Coefficient of Form Resistance;

Cr - Cf*[ 1.5(D/L)^1.5 + 7(D/L)^3 + 0.002(Cp-0.6)].

Cp - Prismatic Coefficient.Cds - Coefficient of Drag, Sail;

Cds - 0.0090.

Cda - Coefficient of Drag, Appendages;

Cda = 0.0060.

Table Cl lists the values of required SHP for each of the submar-ines, for speed ranges of which each is capable.

C-1

-C2-

REQUIRED SHP KILO WALRUS RUBIS BARBEL TYPESUBMERGED TRANSITS HP HP HP HP 2400

2 6.531857 6.392620 6.069771 5.365803 6.0294932.5 12.51668 12.26146 11.63246 10.27074 11.56157

3 21.30373 20.88531 19.80046 17.46533 19.688493.5 33.40885 32.77371 31.05360 27.36876 30.88945

4 49.34248 48.43113 45.86670 40.39554 45.638814.25 58.90326 57.82973 54.75547 48.20864 54.491274.5 69.61058 68.35792 64.71045 56.95628 64.40695

4.75 81.52711 80.07769 75.78993 66.68930 75.444115 94.71529 93.05085 88.05200 77.45831 87.66084

5.25 109.2373 107.3390 101.5545 89.31378 101.11505.5 125.1554 123.0036 116.3554 102.3060 115.8644

6 161.4269 158.7072 150.0821 131.9013 149.47936.5 204.0230 200.6502 189.6910 166.6439 188.9644

7 253.4347 249.3190 235.6389 206.9313 234.77677.5 310.1508 305.1979 288.3806 253.1592 287.3713

8 374.6580 368.7695 348.3692 305.7217 347.20158.5 447.4415 440.5147 416.0558 365.0112 414.7190

9 528.9845 520.9128 491.8903 431.4188 490.374010 720.2750 709.5777 669.7949 587.1454 667.890711 952.3668 938.5714 885.6538 776.0041 883.326812 1229.076 1211.681 1143.018 1001.079 1140.23913 1554.202 1532.680 1445.424 1265.439 1442.16814 1931.526 1905.321 1796.389 1572.139 1792.64015 2364.813 2333.346 2199.419 1924.219 2195.16716 2857.817 2820.483 2658.007 2324.708 2653.24817 3414.277 3370.449 3175.632 2776.624 3170.37118 4037.921 3986.949 3755.764 3282.974 3750.01519 4732.466 4673.679 4401.863 3846.757 4395.64620 5501.617 5434.322 5117.377 4470.960 5110.72421 6349.071 6272.557 5905.747 5158.565 5898.69822 7278.516 7192.050 6770.407 5912.545 6763.01123 8293.630 8196.462 7714.778 6735.863 7707.09524 9398.085 9289.445 8742.279 7631.478 8734.37825 10595.54 10474.64 9856.318 8602.342 9848.279__

LITERATURE/MODEL KILO WALRUS RUBIS BARBEL TYPECORRELATION 2400

ADVERTISED SHP 4000 ? 10000 3150 5400PREDICTED SPEED 18 * 25.1 17.8 20.S

. , .. . . .o . .o .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

ADVERTISED SPEED 25 20 25 21 20PREDICTED SHP 10596 5434 9856 5159 5110

LITERKTURE/MODELCORRELATION: UNSAT N/A SAT LN-AT CAT

TABLE CI: Calculated values of required shaft horsepower ,CHP) aEa function of speed. The lower part of the tableindicates the correlation of the calculated data withthat. found in the literature. (Sheet one of two).

-c3-

REQUIRED SHP TYPE TYPE SAUR0 VASTER- MIDGETSUBMERGED TRANSITS 1700 HP 2000 HP HP GOTLAND HP 100

2 5.662832 4.733628 4.2898S7 3.103136 0.8496412.5 10.84755 9.047344 8.212617 5.927847 1.622428

3 18.45759 15.36660 13.96739 10.06407 2.7532223.5 28.93865 24.05591 21.88989 15.7496b 4.307059

4 42.73170 35.47532 32.31210 23.21952 6.3479674.25 51.00693 42.32031 38.56350 27.69627 7.5708q44.5 60.27376 49.98122 45.56295 32.70609 8.939301

4.75 70.58630 58.50212 53.35116 38.27772 10.46102S 81.99847 67.92690 61.96871 44.43978 12.1438S

5.25 94.56402 78.29930 71.45603 51.2207? 13.995565.5 108.3365 89.66289 81.85342 58.64916 1b.02390

6 139.7161 115.5373 105.5390 75.56124 20.6413t.5 176.5632 145.8963 133.3458 95.40150 2t.0575?

7 219.3013 181.0838 165.5924 118.3944 32.333807.5 268.3526 221.4422 202.5958 144.7630 39.53078

8 324.1371 267.3123 244.6719 174.7294 47.709028.5 387.0734 319.0333 292.1352 208.5147 56.92878

9 457.5786 376.9430 345.2991 246.3389 67.2500410 622.9573 512.6739 469.9769 334.9811 91.4359211 823.5842 677.1839 621.1921 442.4015 120.742212 1062.751 873.1349 801.4175 570.3344 155.641613 1343.736 1103.173 1013.113 720.5039 196.603714 1669.800 1369.933 1258.727 894.6251 244.096015 2044.190 1676.035 1540.698 1094.405 298.583616 2470.145 2024.088 1861.454 1321.544 3o0.529617 2950.887 2416.691 2223.416 1577.734 450.395018 3489.632 2856.433 2628.995 1864.661 508.639519 4089.584 3345.894 3080.594 2184.005 595.720620 4753.938 3887.647 3580.o12 2537.441 tQ2.094821 5485.882 4484.254 4131.437 292c,.637 798.21Vd22 6288.595 5138.271 4735.455 3353.259 Q14.540423 7165.247 S52.249 5395.043 3818.pbi 1041.51724 8119.004 6628.729 6112.574 432S.414 1179.59925 9153.021 7470.247 6890.414 4874.252 1329.235

LITERATURE/MODEL TYPE TYPE SAUR0 VA~STER- MIDGETCORRELATION 1700 2000 GOTLAND 100

ADVERTIZED SHP 0844 7500 z21L ? 42PREDICTED SPEED 24.7 :5 19.1

PREDICTED SHP ~ 15 747) 2223: S53

'G0RRELATION: LAT !o TAJ

7A-BLE :1: C~icui~ted al1ues r reuiooL t moh,~ e :0 - Ea fumotacr~ c, opeec. T&s loe Part :- tn Al

tJat found in tle literatur2. rtheet :1j-

COPY available to DTIC does nolpezmij Iuly legible Zeproductiag

-D1-

APPENDIX D: CALCULATION OF ADDED RESISTANCE AND REQUIREDSHAFT HORSEPOWER WHILE SNORKELING

When the submarine operates near the free surface of the ocean,it generates gravity waves. Generating the gravity waves requirespower, which must be supplied by the submarine if it is to remainat the sane speed as it had when transiting more deeply submerged.The power increase is not great, unless the submarine is operatingat Froude numbers greater than about 0.6, or submergence depthless than one tenth of its length. Reference (16) lists a chartand provides a methodology for determining the added resistance co-efficient due to operating close to the surface, Cw, as a functionof Froude number, length-to-diameter ratio, and submergence ratio(operating depth divided by overall length). The calculations forthe computation of Cw are as follows:

(1). Enter chart with submergence ratio and Froudenumber.

(Ch#)(2). Cw = ----------------------- EQN D-1

4[ (L/D) -1. 3606] * (L/D) ̂2

(3). SHPw - 0.00872(V^3) (WS) (Cw) EQN D-2

where:Cw - Coefficient resistance due gravity wave

generation.(L/D) - Length-to-Diameter ratio.SHPw = The additional shaft horsepower required due to

the operation of the submarine near the surface.h/L - Submergence ratio: "h" is the depth of the submar-

ine axis below the mean surface position; "L" islength overall.

Ch# - The number obtained from chart, Reference(16).

The results of the calculations for each of the submarines areas listed in Table D1.

D-1

-D2-

REQUIRED SHP KILO WALRUS RUBIS BARBEL TYPESNORKELING 2400

2 6.627676 6.475601 N/A 5.455644 6.0892202.5 12.71367 12.43206 N/A 10.45545 11.68436

3 21.67818 21.20959 N/A 17.81642 19.921903,5 34.05752 33.33546 N/A 27.97696 31.29379

4 50.47214 49.40943 N/A 41.45472 46.342964.25 60.35502 59.08698 N/A 49.56983 55.396204.5 71.44879 69.94983 N/A 58.67981 65.552764.75 83.95927 82.18397 N/A 68.96971 76.96015

5 98.02483 95.91696 N/A 80.56136 89.723785.25 113.5246 111.0518 N/A 93.33360 103.78745.5 130.6092 127.7267 N/A 107.4195 119.2640

6 170.1414 166.2541 N/A 140.0721 154.91136.5 218.5651 213.2439 N/A 180.2787 198.0289

7 276.7868 269.5422 N/A 228.8264 249.33287.5 343.1280 333.7566 N/A 284.0789 307.9270

8 420.4898 408.4604 N/A 348.6940 375.76988.5 510.1577 494.8278 N/A 423.8146 453.8120

9 613.5423 594.1409 N/A 510.7010 543.081510 884.1761 851.5181 N/A 740.8206 770.055211 N/A 1156.559 N/A N/A N/A12 N/A 1551.290 N/A N/A N/A13 N/A N/A N/A N/A N/A14 N/A N/A N/A N/A N/A15 N/A N/A N/A N/A N/A

Table D1: The calculated values of required shaft horsepower whenoperating at snorkel depth. (Sheet one of two).

-D3-

REQUIRED SHP TYPE TYPE SAURO VASTER- MIDGETSNORKELING 1700 2000 GOTLAND 100

2 5.725325 4.798516 4.335458 3.160754 N/A2.5 10.97603 9.180750 8.306371 6.046307 N/A

3 18.70180 15.62018 14.14560 10.28924 N/A3.5 29.36171 24.49518 22.19860 16.13973 N/A

4 43.46846 36.24032 32.84972 23.89881 N/A4.25 51.95376 43.30344 39.25441 28.56926 N/A4.5 61.47263 51.22606 46.43778 33.81147 N/A

4.75 72.17254 60.14917 54.50866 39.74025 N/A5 84.15693 70.16811 63.54377 46.42991 N/A

5.25 97.36018 81.20264 73.49642 53.79887 N/A5.5 111.8935 93.35619 84.44896 61.92870 N/A

6 145.3997 121.4387 109.6864 80.80153 N/A6.5 186.0475 155.7441 140.2666 104.1462 N/A

7 234.5315 196.8978 176.7060 132.4368 N/A7.5 289.8602 243.7743 218.2902 164.5932 N/A

8 354.0284 298.3494 266.4839 202.2895 N/A8.5 427.9766 361.5045 321.9828 246.2278 N/A

9 512.7268 434.2053 385.5414 297.1861 N/A10 729.8528 623.6671 547.9798 433.5398 N/A11 987.7510 847.6439 740.9866 N/A N/A12 1318.511 1138.699 N/A N/A N/A13 1723.108 1497.088 N/A N/A N/A14 2166.189 1885.352 N/A N/A N/A15 2626.976 2281.162 N/A N/A N/A

Table DI: The calculated values of required shaft horsepower whenoperating at snorkel depth. (Sheet two of two).

-El-APPENDIX E: CALCULATION OF ENDURANCE RANGE

The fuel endurance range is calculated at the snorkel depth, anddepends upon the following factors:

(1) Diesel engine specific fuel consumption.(2? Bunker fuel load.(3) Transit speed.(4) Speed vs Power relation.(5) Hotel electric load.(6) Complement.(7) Water temperature, (affects heating and/or A/C load).(8) Sea State, (to the extent that it affects snorting).

All of these factors may play a part in determining the endurancerange of the diesel-electric submarines, but only items (1)through (5) above can be estimated with a degree of accuracy giventhe data available in the literature.

It should be noted that in the matter of endurance range, "biggeris better". The reason for this economy of scale is that the dragforce on a submerged body is proportional to its wetted surfacearea, but the fuel capacity is proportional to its internal volume.

The following relation, adapted from Reference (3), may be used tocalculate endurance range:

Rf - 2240((F)(0.8)(Nem)(V)]/[(SFC)(SHP + 1.34*Lh)) EQN E-1

where:Rf - Endurance Range based on fuel, Nm.F - Bunker fuel load, Ltons.Nem - Efficiency of electro-mechanical energy conversion;

Nem is assumed to be 0.95.

V - Speed (submerged), Kts.SFC - Diesel specific fuel consumption, lbs/HP-Hr;

SFC values are estimated in Appendix P.

SHP - Shaft horsepower, HP.Lh - Hotel electric load, KW;

Lh values are estimated in Appendix M.

2240 - Conversion factor, (lbs/Lton).0.8 - Proportion of bunker fuel consumed.1.34 - Conversion factor, (HP/KW).

Table E-i lists the fuel endurance range, calculated at snorkel

depth.

E-1

-E2-

"It may be mathematically proven that the maximum endurance rangeoccurs at the speed for which the shaft horsepower required isexactly half of the hotel electric power requirement, (for a con-stant hotel power load)."

- Harry Jackson, P.E., CAPT USN, (Ret.)24 April, 1988

The following is one way of proving CAPT Jackson's statement:

Pt - (SHP) + (Lh). EQN E-2

where:Pt - Total power required at a given speed, HP.SHP - Shaft Horsepower required at a given speed, HP.Lh - Hotel electric load, assumed constant, HP.

Equation E-2 quantifies the power required at a given speed.The SHP is a function of speed, as shown by Equations C-1 andC-2, and can be approximated by the following expression:

SHP - (Kv)(V^3) EQN E-3

where:Kv - A constant, determined from EQN C-1 and C-2.

Equation E-3 is suitably accurate within a suitable neighbor-hood of the point of evaluation of Kv. The maximum endurancerange will occur at the speed for which the energy expenditureper mile is the least. The energy per mile is related to thepower output by this expression:

E/Nm - Pt/V - (Kv)(V^2) + (Lh)/V EQN E-4

where:E - Total Energy required by the ship at some

speed, HP-Hour.Nm - Nautical miles.

The energy per nautical mile will have a minima where its slopeis zero, a point which may be found by:

(E/Nm) - 2(Kv)V - (Lh)/(V^2) - 0. EQN E-5

Rearranging Equation E-5:

Lh - 2(Kv)(V^3) - 2(SHP). EON E-6

Which was to be proved.

E-2

-E3-

FUEL RANGE KILO WALRUS RUBIS BARBEL TYPE(SNORKELING) 2400

BUNKER FUEL, Lton 270 275 19.4 130 186.7

MECH/ELEC EFFCNCY 0.95 0.95 0.95 0.95 0.95HOTEL LOAD, Kw 131.32 124.7981 129.784 94.38 115.94FUEL USED, % 80 80 100 Bo 80

SPEED, Kts ENDURANCE RANGE, Nm2 6828.326 7376.931 765.1887 4612.769 5438.270

2.5 8270.424 8929.778 935.3956 5566.245 6563.0413 9491.796 10240.78 1088.135 6356.902 7550.171

3.5 10447.52 11261.99 1220.110 6955.936 8304.9774 11111.65 11967.48 1329.747 7349.901 8829.774

4.25 11335.22 12203.45 1376.587 7472.756 9007.2784.5 11489.80 12365.61 1418.630 7549.660 9131.270

4.75 11573.55 12452.93 1455.785 7579.379 9202.0185 11589.68 12469.40 1488.519 7564.702 9222.793

5.25 11553.28 12430.53 1518.732 7517.778 9203.5535.5 11467.88 12340.61 1547.090 7441.110 9147.898

6 11168.16 12028.46 1601.826 7211.156 8943.7526.5 10712.26 11559.82 1659.270 6888.048 8634.084

7 10162.06 10998.98 1735.200 6515.530 8262.8327.5 9616.423 10445.07 6164.247 7893.334

8 9057.255 9882.734 5815.509 7521.1038.5 8505.609 9333.846 5481.798 7162.206

9 7976.095 8813.627 5171.633 6828.15710 6909.486 7786.273 4560.516 6196.24511 7145.19312 6673.183131415

TABLE El: Calculated values of endurance range based upon bunker fuelloadout, at snorkel depth. For RUBIS, values reflect rangeon emrgency diesel. (Sheet one of two).

-E4-

FUEL RANGE TYPE TYPE SAURO VASTER- MIDGET(SNORKELING) 1700 2000 GOTL'D 100

BUNKER FUEL, Lton 319 236 144 40 4

MECH/ELEC EFFCNCY 0.95 0.95 0.95 0.95 0.95HOTEL LOAD, Kw 114.996 108.2 88.137 63.882 15FUEL USED, % 80 80 80 80 80

SPEED, Kts ENDURANCE RANGE, Nm2 9499.596 7579.153 5665.119 2088.014 875.6985

2.5 11522.91 9226.273 6877.205 2531.192 1055.6913 13253.47 10664.33 7919.184 2908.679 1204.146

3.5 14631.38 11846.46 8755.996 3206.897 1315.4004 15622.82 12741.29 9367.636 3417.363 1387.308

4.25 15974.44 13079.28 9589.354 3489.808 1408.8704.5 16234.37 13346.19 9757.475 3541.290 1421.450

4.75 16401.71 13539.13 9871.493 3570.673 1425.7095 16481.18 13660.13 9934.110 3578.675 1422.422

5.25 16490.35 13723.52 9955.493 3570.548 1412.4295.5 16434.69 13732.24 9938.861 3547.081 1396.604

6 16155.11 13602.10 9807.015 3458.826 1350.8946.5 15678.34 13287.93 9559.896 3318.002 1291.741

7 15082.63 12853.73 9243.734 3145.032 1224.5937.5 14488.89 12412.32 8930.694 2975.464 1153.708

8 13885.91 11947.53 8615.637 2800.381 1082.2008.5 13304.94 11487.99 8318.752 2626.659 1012.211

9 12769.76 11056.54 8056.444 2459.172 945.115210 11764.03 10200.01 7602.278 2113.869 822.414211 11337.42 9912.255 7622.481 716.415612 10850.59 9321.353 626.342713 9454.215 7670.309 550.278114 6627.458 5355.612 486.079215 4775.783 3911.715 431.7544

TABLE El: Calculated values of endurance range based upon bunker fuelloadout, at snorkel depth. MIDGET 100 calculated at deepsubmerged depth. (Sheet two of two).

-Fl-

APPENDIX F: LEAD-ACID BATTERY POWER AND ENERGYCHARACTERISTICS

F.l. Type of Battery

It is commonly held that the type of secondary storage batter-ies in modern diesel-electric submarines are of the lead-acidvariety, although the literature did not confirm this. Some ofthe reasons for the popularity of lead-acid cells in submarinesare as follows, from Reference (20):

(1) Lowest cost (by a factor of ten) per KW-Hr of allstorage batteries.

(2) Reasonably high power to volune density.(3) The weight is beneficial to stability.(4) Maintainance is available throughout the world.(5) Good safety record.

Reasons for the popularity of lead-acid batteries insubmarine propulsion.

F.2. Power and Energy Capacity

The energy available from a lead-acid cell is dependent upon therate of energy extraction - the power demanded of the cell rela-tive to the cell's capacity. This is because the internal elec-trical resistance of the lead plates and the internal fluid re-sistance of the ions in the acid electrolyte both increase withincreasing power demands. This effect has been minimised in state-of-the-art batteries manufactured by such firms as Varta and Hagenof West Germany, and Gould of the U.S. Below are listed the mostimportant factors concerning the battery capacity are, from Refer-ence (20):

(1) Battery nominal energy capacity.(2) Battery design, (geometry and structure).(3) Maintainance state of the battery.(4) Number of previous deep-discharge cycles on the

battery.(5) Battery internal resistance.(6) Battery power vs energy relation.(7) Temperature of discharge.

Factors contributing to battery capacity.

For a typical lead-acid storage cell of the type used in submar-ines, the total energy capacity, when discharged at the 100-hourrate, is approximately 23.5 KW-Hrs, calculated from Reference(16). The available energy capacity of the battery is reducedfor faster discharge rates. A numerical curve-fit describing the

F-i

-F2-

energy capacity of this typical cell, as a function of service-life, may be descibed by a sum of first-order transients, givenby Equation F-i.

Ec - (23KW-Hrs)*[0.3030(1-exp(-Td/26))+0.2597(l-exp(-Td/2.7))+0.2424(1-exp(-Td/0.41))+O.1948(l-exp(-Td/O.05))] EQN F-l

where:Ec - The energy in a single cell, KW-Hrs.Eb - The energy in the entire battery, KW-Hrs.Td - Service life, Hrs. The time required to discharge

the battery to a given end-voltage at a given dis-charge rate.

#C = The number of standard cells in the battery.

Table Fl gives the calculated values of battery energy capacityfor each of the submarines, at discharge rates equal to thatnecessary to maintain the corresponding speed. Figure F-Igraphically displays the information of Table Fl.

F.3. Other Factors

A well-designed battery will minimize internal resistance andallow more complete energy utilization at high discharge rates.One way of reducing the internal resistance is to use sandwichanode and cathode plates, which have internal cores of copperwhich is about fifteen times more conductive than lead at roomtemperature, References (20) and (22). This decreased resistanceis very important in reducing the ampere heating of the leadplates at high discharge currents. The battery may also be pro-vided with its own cooling system to prevent overheating. Thebattery room should also be equipped with a separate ventilationsystem, to safely duct away any evolved hydrogen during chargingperiods.

F-2

-F3-

SUBMARINE NAME

AVAILABLE KILO WALRUS RUBIS 8ARBEL TYPEBATTERY ENEPGY 2400

BATTERY ENERGY KW-Hrs KW-Hrs KW-h!rs KW-Hr-@ 100 Hr Rate 11280 112 0 N/A 1 ']44 11280

HOTEL LOAD, Kw 131 .32 124. 781 129. 84 94. -i ,4

DICCHARGE DEPTH C.O .o0 0.80 0.a0 0). S0

'-n rD Kt= A ....... = D TT R'7 ENER '' - -

30% Deptr, cf Diszc-ar.c2 8795.Q5 8824. 135 -?so401.77S 081.0

2.5 8775 .0 8835. 1. 27 N3/A .31 1? 8345.1363 8744.90 07-N./3,2 / ' . 3819.562

r-'IN A4- -732. 6613.5 8702.218 '3735.274 N/ 9-. 2 65¢ 872.6

4 8644.727 8679.683 N/A 9312.742 8731.8834.25 8609.823 8645.642 N/A 9289 .242 8700 .5244.5 8570.593 8607.20 N/A q261.723 86t4.851

4.75 8526.963 85o4.257 N/A 9229.821 8t24.6935 8478.956 8516 .7 2 N/A 919.23 3 8579.96b

5.25 8426.695 34,4.?01 N/A51.74 3530.6885.5 8370.410 8408.790 N/9A 105.202 3476.991

6 8247.203 8285.287 N/A 8997.166 S357.4416.5 8113.035 8149.96l N/A 8870..,5 r 2-24. 562

7 7972.445 8007.481 N/A 372?.; S 08. 84.7.5 7829.967 732=.b27 N/A 8578. 008 7'Z7 .212

S17b89.299 771r). 408 N/A 8422 L 7'2 08

8. 75 1 -55'74 1r NiA 2667- . 1 650.-139 7420.914 744,.56 4 N/A 3115. 0'9 7514.b7410 7167.943 7191.117 Ni 78372.

11 65917 .337 6940 023 N/A 7 7 -c .- 09 .95 -12 6657.415 6680 c.3 N/A 721.232 75t.52Z-

13 6386.219 6410 077 N/A 70t5.2'08 , ' 6214 6111.165 &13 1 N" //' A '"15 5843 308 N/8A6 i4 N/ t52' .1 ?a C,

1 t 550 7 06 5 =2 N/ t'2 .' 1 2117 5354 r)3[ 575. 150 A O0 "T. A " (3 C,18 51 1 98c 5151 930 A 7,7 -. t

2 ,: -20 .: 2 . 4 ,'; :PI Z

T 7 - - -- - - T 27 Z -- --7 -- 7- - 2 - 7 . . .- - - _-- - - T -IT T T T - - -.. . . . . . . . . . . . . . . . .

, .. /, e e d ,. (D11t E:~ . , :. 1:: . ~~- . Epq -{

-F4-

SUBMARINE NAME

AVAILABLE TYPE TYPE SAURO VASTER- MIDGETBATTERY ENERGY 1700 2000 GOTL'D 100

BATTERY ENERGY KW-Hrs KW-Hrs KW-Hrs KW-Hrs KW-Hrs@ 100 Hr Rate 22560 16920 6956 3948 352.5

HOTEL LOAD, Kw 114.996 108.2 88.137 63.882 15DISCHARGE DEPTH 0.80 0.80 0.80 0.80 0.80

SPEED, Kts AVAILABLE BATTERY ENERGY, KW-Hrs80% Depth of Discharge

2 18030.45 13495.65 5389.971 2989.427 233.54592.5 18027.16 13490.10 5376.162 2979.089 232.3389

3 18021.60 13481.19 5355.592 2964.042 230.65813.5 18012.44 13467.48 5326.847 2943.625 228.4918

4 17997.61 13446.91 5288.653 2917.437 225.85174.25 17987.17 13433.25 5265.713 2902.156 224.36044.5 17974.09 13416.83 5240.126 2885.46, 222.7579

4.75 17957.82 13397.21 5211.893 2867.434 221.04565 17937.76 13373.97 5181.070 2848.174 219.2238

5.25 17913.24 13346.65 5147.779 2827.819 217.29225.5 17883.57 13314.80 5112.201 2806.526 215.2501

6 17806.06 13235.94 5035.190 2761.832 210.83306.5 17700.19 13134.83 4952.456 2715.515 205.9839

7 17562.39 13010.35 4866.744 2668.821 200.74917.5 17391.42 12863.21 4780.601 2622.575 195.2198

8 17188.89 12696.05 4695.922 2577.074 189.52388.5 16959.13 12513.14 4613.680 2532.127 183.8000

9 16708.63 12319.75 4533.911 2487.219 178.166410 16176.10 11923.23 4378.615 2395.095 167.393311 15648.13 11542.15 4221.627 2297.458 157.139912 15159.23 11192.34 4057.175 2195.212 146.895713 14714.75 10869.87 3886.142 2092.662 136.311514 14299.97 10560.70 3714.622 1994.420 125.523115 13894.78 10251.05 3549.555 1902.641 115.038916 13484.28 9933.378 3394.779 1816.432 105.359917 13063.01 9607.601 3249.773 1733.144 96.6560118 12634.25 9279.318 3111.019 1650.071 88.6610719 12206.74 8956.557 2974.265 1565.66420 11790.44 8646.413 1480.00221 11392.88 8352.70922 11017.02 8075.36123 10661.27 7811.25624 10320.92 7555.81125 9990.057 7304.423

TABLE FI: Available energy from each submarine battery at severa1 tran-sit speeds, 80% depth of discharge. (Page two cf two).

-F5-Battery Power Output, (Submerged)

101

08- - - - - - - - - - - - - -

1- - - - - -

a-*

a o in 14 Is 22 20

Fiur F1:Toabattery power output (Siubmsered)8%DD

-F6.Available Battery Energy

14 - - -

IL 41*- -ARU - * - U -i - -E - E2

14-

13

SPEED, ow+ ME u 240 SAUmi D iI l~2

Figur F -2 Available Battery Energyatvrosped,8%D.

-G 1-

APPENDIX G: CALCULATION OF BATTERY ENDURANCE RANGE

Once the battery power and energy capacities are determined,the submerged endurance as a function of speed may be calcula-ted. The battery range falls off with increasing speed evenmore quickly than the fuel endurance range, because the subma-rine is fighting the non-linear dissipative effects of batteryinternal resistance as well as the non-linear external resis-tance of the sea.

The maximum range which a diesel-electric submarine may achievedepends upon elements (1) through (8) detailed in Appendix E, andalso upon factors which relate to the submarine's battery capacity.The following relations, adapted from References (3) and (20), maybe used to calculate battery endurance range:

Mb = (V) (Td) EQN G-1

Td - (DoD) (Eb)/(SHP/1.34)+Lh EQN G-2

Eb - Eb(Td) (Given by EQN F-l) EQN G-3

where:Mb - Endurance range on batteries, Nm.Td - Service life, Hrs. The time required to discharge

the battery to a given end-voltage at a given dis-charge rate.

V - Speed (submerged), Kts.DoD - Depth of discharge, Non-Dimensional;

DoD is taken to be 0.80,(80% discharged).

Eb - Battery energy at the specific discharge rate,(A function of Td), KW-Hrs.

SHP - Shaft Horsepower at the speed, HP.Lh = Hotel electric load, KW. See Appendix M.1.34 = Conversion factor, HP/KW.

Note that because Eb, Td, and Mb are interdependent, EquationsG-1 through G-3 must be solved iteratively. The results of theiterative calculations are listed in Table G-l.

The procedure is to iterate beween Equations G-2 and F-1 to solvefor Td, then evaluate G-1 to find the range.

Table Gi lists the numerical values resulting from this procedure,for the appropriate speed ranges for each submarine.

G-1

-G2-

SUBMARINE NAME

ENDURANCE RANGE KILO WALRUS RUBIS BARBEL TYPE(BATTERY) 2400

SPEED, Kts2 129.1569 136.2082 27.54910 191.1196 147.1608

2.5 155.9630 164.3386 33.25911 230.0709 177.51763 178.2041 187.5513 37.99322 261.8180 202.5429

3.5 194.9291 204.8429 41.55321 285.0229 221.16034 205.6549 215.7262 43.84194 299.1382 232.8539

4.25 208.7679 218.7763 44.51084 302.8524 236.12004.5 210.4480 220.3103 44.87703 304.4705 237.75104.75 210.7816 220.4248 44.95829 304.1409 237.8517

5 209.8777 219.2402 44.77664 302.0408 236.55175.25 207.8625 216.8942 44.35718 298.3668 233.99915.5 204.8727 213.5348 43.72687 293.3259 230.3527

6 196.5362 204.3850 41.94480 279.9795 220.43256.5 185.9728 192.9699 39.64785 263.6053 208.0579

7 174.1616 180.3253 37.03366 245.6049 194.34537.5 161.8850 167.2717 34.26950 227.1004 180.1849

8 149.7087 154.3967 31.48807 208.9150 166.22048.5 137.9987 142.0751 28.78729 191.5936 152.8671

9 126.9597 130.5109 26.23251 175.4477 140.354410 107.1760 109.9059 21.68530 147.0886 118.135711 90.37202 92.51592 17.90602 123.6912 99.4774812 76.20073 77.91603 14.79010 104.4173 83.8663913 64.31188 65.70095 12.21102 88.43434 70.8129714 54.41372 55.54604 10.07317 75.11599 59.9390915 46.24085 47.16821 8.310787 64.01748 50.9364416 39.52370 40.28832 6.872713 54.79870 43.5269317 33.98994 34.62708 5.711075 47.16347 37.4238018 29.38857 29.92661 4.777000 40.83357 32.3637819 25.97257 4.022209 28.1188120 22.60194 3.403562 24.5098321 2.88677422 2.44723323 2.06851924 1.74011725 1.455271

TABLE G: Calculated values of each submarine's endurance range onbatteries alone, 80% depth of discharge. (Sheet cne of two).

-G3-

SUBMARINE NAME

ENDURANCE RANGE TYPE TYPE SAURO VASTER- MIDGET(BATTERY) 1700 2000 GOTL'D 100

SPEED, Kts2 302.4685 241.5707 118.0259 90.32605 29.88167

2.5 366.1343 293.3861 142.5852 109.0456 35.837503 419.8546 337.9660 163.0220 124.5662 40.58154

3.5 461.5464 373.6454 178.4682 136.2320 43.915004 490.1134 399.3912 188.4733 143.7189 45.78124

4.25 499.4450 408.4302 191.4304 145.9008 46.186364.5 505.5959 414.9551 193.0821 147.0919 46.26667

4.75 508.7283 419.0537 193.5052 147.3553 46.049545 509.0492 420.8519 192.7975 146.7695 45.56589

5.25 506.7977 420.5063 191.0723 145.4244 44.848595.5 502.2342 418.1963 188.4533 143.4166 43.93107

6 487.2548 408.4709 181.0471 137.8071 41.625616.5 466.2484 393.2991 171.5806 130.6975 38.892757 441.1810 374.2651 160.9425 122.7391 35.93971

7.5 413.7410 352.7973 149.8417 114.4356 32.932128 385.3042 330.1046 138.7904 106.1409 29.99403

8.5 356.9394 307.1529 128.1200 98.08144 27.210299 329.4335 284.6683 118.0180 90.38883 24.6305310 278.9504 242.9399 99.79719 76.34026 20.1428111 235.9184 206.9302 84.20427 64.17872 16.4830512 200.3205 176.7700 70.99404 53.86472 13.4900913 171.1339 151.7062 59.89765 45.27508 11.0219714 147.0841 130.7787 50.67037 38.22104 8.98740115 127.0458 113.1491 43.06617 32.45918 7.33016916 110.1652 98.18608 36.82178 27.72909 6.00352817 95.83653 85.43737 31.67161 23.79750 4.95311418 83.63180 74.57120 27.37721 20.48239 4.11683219 73.23236 65.32347 23.74723 17.6543520 64.37877 57.46281 15.2263621 56.84130 50.7745822 50.40887 45.0600923 44.89010 40.1427324 40.11850 35.8736125 35.95604 32.13314

TABLE GI: Calculated values cof each submarine's endurance range onbatteries alone, 80% depth of discharge. (Sheet two of two).

APPENDIX H: CALCULATION OF INDISCRETION RATEAND INDISCRETION INTERVAL

The necessity to charge the storage batteries requires the diesel-electric submarine to operate, for some portion of time, eitheron the surface or snorting near the surface. The ratio of thetime spent on or near the surface to the total time spent in tran-sit is called the indiscretion rate, and it is desirable to keepit as low as possible.

(1) Electric generator/alternator power capacity.(2) Number and size of cells in the battery.(3) Type of battery.(4) Ability to control the charging parameters for opti-

mal charging profile, (closed-loop control).(5) Vessel transit speed and associated SHP.(6) Hotel electric load.

Factors affecting indiscretion rate.

Calculation of the indiscretion rate may be performed as follows:

IR - Tr/(Tr + Td) EQN H-I

(DOD)(Eb)Tr - ------------------------------EQN H-2

(Pdg - (SHP/1.34) - Lh)(Nbc)

where:IR - Indiscretion rate, non-dimensional fraction.Tr - Time to recharge battery, Hrs.Td - Battery service life, evaluated at a given speed,

Hrs.DoD - Depth of discharge of the battery.

DoD - 0.8, non-dimensional.

Eb - Battery energy capacity at the rate ofdischarge, KW-Hrs.

Pdg - Power of the diesel/generators, KW.SHPw - Shaft horsepower required at the transit

speed, operations near the surface, HP.Lh - Hotel electric load, KW.Nbc - Average efficiency of electrical-to-chemical

energy conversion in the charging of the battery.

Nbc - 0.7 - 0.8, Reference (20),

assumed to equal 0.75 for this study.

The calculated values of indiscretion rate are listed in TableHi. Note that the Shaft horsepower used in Equation H-2 is the"near the surface" value, since the submarine is operating nearthe surface when snorkeling to recharge its batteries. The

H-i

-H2-speed range Listed in Table Hi extends naturally, only to eachsubmarine's max snorkel speed.

The indiscretion interval at a given speed is the duration oftime a submarine may transit at the speed, while completely sub-'merged and without snorkeling. It is actually another name forthe battery service life at the given speed. Table H2 lists thecalculated values of indiscretion interval for each submarine'ssubmerged speed range.

Note that the average electrical-to-chemical energy conversionefficiency is used. It is suitable for comparison purposes, butassumes a constant charging rate. The actual charging rate andcharging efficiency is a function of the recharge power, sincethe same internal resistance factors are at work in the recharg-ing process as in the discharging process. So shorter rechargetimes are less efficient (and hence longer) than indicated inthis first-order calculation.

H-2

-H3-

SUBMARINE NAME

INDISCRETION KILO WALRUS RUBIS BARBEL TYPERATE 2400

SPEED, Kts INDISCRETION RATE, Fraction2 0.040950 0.033859 N/A 0.036584 0.064304

2.5 0.042372 0.035066 N/A 0.037974 0.0665893 0.044472 0.036852 N/A 0.040022 0.069962

3.5 0.047389 0.039335 N/A 0.042858 0.0746444 0.051272 0.042643 N/A 0.046622 0.080866

4.25 0.053623 0.044648 N/A 0.048898 0.0846304.5 0.056276 0.046911 N/A 0.051463 0.0888714.75 0.059251 0.049452 N/A 0.054338 0.093623

5 0.062571 0.052289 N/A 0.057547 0.0989215.25 0.066256 0.055440 N/A 0.061109 0.1047945.5 0.070329 0.058926 N/A 0.065049 0.111275

6 0.079723 0.066978 N/A 0.074158 0.1261966.5 0.090938 0.076608 N/A 0.085084 0.143950

7 0.104135 0.087959 N/A 0.098021 0.1647547.5 0.119408 0.101130 N/A 0.113094 0.188694

8 0.136911 0.116251 N/A 0.130488 0.2159318.5 0.156766 0.133431 N/A 0.150339 0.246549

9 0.179105 0.152784 N/A 0.172774 0.28060810 0.232437 0.198917 N/A 0.226609 0.36025711 0.254948 N/A12 0.322926 N/A13 N/A14 N/A15 N/A16 N/A17 N/A18 N/A19 N/A20 N/A21 N/A22 N/A23 N/A24 N/A25 N/A

TABLE Hi: Calculated values of indiscretion rate at various speeds.Note that only speeds up to the maximum snorkel speed arelisted, since the batteries may be charged only while sur-faced or snorkeling. (Sheet one of two).

-H4-

SUBMARINE NAME

INDISCRETION TYPE TYPE SAURO VASTER- MIDGETRATE 1700 2000 GOTL'D 100

SPEED, Kts INDISCRETION RATE, Fraction2 0.035838 0.041076 0.057321 0.057359 N/A

2.5 0.036997 0.042264 0.059275 0.059352 N/A3 0.038700 0.044008 0.062158 0.062287 N/A

3.5 0.041048 0.046411 0.066158 0.066354 N/A4 0.044144 0.049582 0.071474 0.071748 N/A

4.25 0.046005 0.051490 0.074690 0.075005 N/A4.5 0.048094 0.053632 0.078312 0.078669 N/A

4.75 0.050425 0.056025 0.082369 0.082768 N/A5 0.053013 0.058683 0.086889 0.087330 N/A

5.25 0.055872 0.061623 0.091897 0.092375 N/A5.5 0.059020 0.064862 0.097419 0.097927 N/A

6 0.066249 0.072309 0.110113 0.110658 N/A6.5 0.074855 0.081190 0.125183 0.125741 N/A

7 0.085001 0.091669 0.142806 0.143362 N/A7.5 0.096830 0.103880 0.163065 0.163592 N/A

8 0.110527 0.118008 0.186119 0.186672 N/A8.5 0.126257 0.134213 0.212083 0.212809 N/A

9 0.144175 0.152640 0.241072 0.242234 N/A10 0.187408 0.197101 0.309386 0.313289 N/A11 0.240259 0.251248 0.390218 N/A12 0.303947 0.316820 N/A13 0.378685 0.394424 N/A14 0.461881 0.480992 N/A15 0.549989 0.572121 N/A16171819202122232425

TABLE Hi: Calculated values of indiscretion rate at various speeds.Note that only speeds up to the maximum snorkel speed arelisted, since the batteries may be charged only while sur-faced or snorkeling. (Sheet two of two).

-H5-

SUBMARINE NAME

INDISCRETION KILO WALRUS RUBIS BARBEL TYPEINTERVAL 2400

SPEED, Kts INDISCRETION INTERVAL, HOURS, (80% DISCHARGE)2 64.57398 68.10035 N/A 95.55879 73.57759

2.5 62.38017 65.73116 N/A 92.02707 71.003753 59.39552 62.51198 N/A 87.27090 67.51031

3.5 55.68707 58.52031 N/A 81.43254 63.183584 51.40541 53.92389 N/A 74.78071 58.20699

4.25 49.11280 51.46832 N/A 71.25471 55.550334.5 46.75641 48.94855 N/A 67.65441 52.82534

4.75 44.36453 46.39511 N/A 64.02281 50.064905 41.96436 43.83718 N/A 60.40002 47.30030

52 5 39.58113 41.30165 N/A 56.82224 44.560355.5 37.23747 38.81245 N/A 53.32102 41.87067

6 32.74365 34.05160 N/A 46.64965 36.726136.5 28.59932 29.67545 N/A 40.53916 31.99617

7 24.86948 25.74957 N/A 35.07023 27.751617.5 21.57538 22.29317 N/A 30.26445 24.01399

8 18.70578 19.29140 N/A 26.10030 20.768478.5 16.22859 16.70787 N/A 22.52835 17.97679

9 14.10102 14.49539 N/A 19.48413 15.5885710 10.71286 10.98578 N/A 14.70179 11.8085611 8.210790 8.405691 N/A 11.23890 9.03859812 6.344672 6.487628 N/A 8.695785 6.98361213 4.941292 5.048126 N/A 6.796511 5.44139714 3.881065 3.961882 N/A 5.358868 4.27553515 3.077707 3.139446 N/A 4.261323 3.39053016 2.465939 2.513653 N/A 3.418984 2.71579117 1.995651 2.033081 N/A 2.769198 2.19740018 1.629179 1.659051 N/A 2.264128 1.79436619 0 1.363428 N/A 0 1.47640820 0 1.126341 N/A 0 1.22182821 0 0 N/A 0 022 0 0 N/A 0 023 0 0 N/A 0 024 0 0 N/A 0 025 0 0 N/A 0 0

Table H2: Calculated values of indiscretion interval as a function ofsubmerged speed. This is the same as the battery dischargetime at a given speed. (Sheet one of two).

-H6-

SUBMARINE NAME

INDISCRETION TYPE TYPE SAURO VASTER- MIDGETINTERVAL 1700 2000 GOTL'D 100

SPEED, Kts INDISCRETION INTERVAL, HOURS, (80% DISCHARGE)2 151.2342 120.7853 58.98672 45.12221 14.93813

2.5 146.4537 117.3544 57.00584 43.57625 14.332383 139.9515 112.6553 54.30961 41.47874 13.52465

3.5 131.8704 106.7558 50.95640 38.87891 12.544694 122.5283 99.84776 47.08008 35.88467 11.44289

4.25 117.5164 96.10118 45.00243 34.28466 10.864954.5 112.3546 92.21217 42.86554 32.64261 10.27902

4.75 107.1007 88.22173 40.69505 30.97849 9.6921225 101.8098 84.17023 38.51571 29.31140 9.110573

5.25 96.53293 80.09622 36.35051 27.65890 8.5398685.5 91.31537 76.03540 34.22010 26.03655 7.984606

6 81.20922 68.07801 30.13209 22.93284 6.9343916.5 71.73067 60.50679 26.35806 20.07671 5.979915

7 63.02610 53.46536 22.95727 17.50754 5.1303517.5 55.16582 47.03825 19.94896 15.23460 4.386905

8 48.16351 41.26146 17.32286 13.24622 3.745252

8.5 41.99348 36.13393 15.05003 11.51864 3.1974039 36.60444 31.62816 13.09216 10.02300 2.733175

10 27.89585 24.29276 9.959791 7.612412 2.01107511 21.44787 18.81106 7.633588 5.811186 1.49505912 16.69398 14.73036 5.893194 4.465660 1.12005413 13.16464 11.66938 4.584501 3.461733 0.84288914 10.50646 9.341067 3.598088 2.711770 0.63665215 8.470181 7.543012 2.852361 2.147554 0.48371516 6.885829 6.136362 2.284675 1.717324 0.37091717 5.637999 5.025463 1.847315 1.383626 0.28750318 4.646802 4.142600 1.505118 1.120591 0.22469619 3.854927 3.437869 1.233151 0.910880 020 3.219499 2.872972 0 0.742793 021 2.707238 2.417705 0 0 022 2.291770 2.048080 0 0 023 1.952161 1.745247 0 0 024 1.671998 1.494654 0 0 025 1.438629 1.285250 0 0 0 a

Table H2: Calculated values of indiscretion interval as a function ofsubmerged speed. This is the same as the battery dischargetime at a given speed. The values given for the MIDGET 100are termed the battery discharge times only since this subdoes not snorkel. (Sheet two of two).

I-Il-

APPENDIX I: ESTIMATION OF WEIGHT GROUPS

The estimation of the weight groups from open literature is dif-ficult. The following empirical relations have been developed togenerate weight values for functional groups which were not foundin the literature.

Wstr - (Dsrf)[0.00055*Id + 0.151 EQN I-I

Wmob - 0.572(#C) + 2.1(SHPi)V0.64 EQN 1-2

Wfb - 0.05(Dsurf) EQN 1-3

Wwep - 0.002(VOLw) + 6(#T) + 5 EQN 1-4

Wc3i - 0.00836(VOLc) EQN 1-5

Wfw - (GPD)(#w)/(300gal/Lton) EQN 1-6

Wss - 0.04(Dstd) + 0.40(Men) EQN 1-7

where:#C - Number of equivalent standard battery cells.#w - Number of days subsistence on water tank alone.#T - Equivalent number of 21" torpedo tubes.Dsrf - Surfaced Displacement, Lton.Dstd - Standard Displacement, Lton.GPD - Gallons of fresh water consumed per day.Id - Immersion depth, meters.SHPi - Installed shaft horsepower.VOLc - Volume of C31 spaces, cu ft.VOLw - Volume of weapons spaces, cu ft.Wc31 - Weight of C31 equipment, Lton.Wfb - Weight of fixed ballast, Lton.Wfw - Weight of fresh water loadout, Lton.Wmob - Weight of the mobility machinery, Lton.Wss - Weight of ship support functional group, Lton.Wstr - Weight of the submarine structure, Lton.Wwep - Weight of weapons functional group, Lton.

Equations I-i and 1-2 are adapted from Reference (15). Equations1-3 through 1-7 were based loosely on the weight values for theBARBEL, with consideration of the variables which contribute tothe weight of a functional group.

After the above equations were evaluated for each submarine, theformula-calculated submerged displacement is compared to the re-ference submerged displacement, and all of the calculated weightsare scaled by a common coefficient in order to bring the calcula-ted displacement equal to the reference displacement.

The computed values for each submarine weight group are shownin-Table 8-1.

I-i

a

-J 1-

APPENDIX J: CALCULATION OF ANAEROBIC DIESEL FUEL/OXYGEN LOAD

The anaerobic diesel cycle developed by Sub Sea Oil Services and used inthe MIDGET 100 in truly an engineering accomplishment. According to theliterature, the submerged endurance range of the MIDGET 100 is unmatchedby all vessels within ten times its displacement. The reason for thisis the relative energy-to-weight and energy-to-volume densities of fueloil/oxygen as compared to lead/acid storage batteries.

Since the propulsion plant is "anaerobic' as far as the atmosphere isconcerned, the combustion oxygen must be carried along with thesubmarine.

The following analysis is taken from Reference (3), and shows that theweight of the required oxygen loaded is approximately three-and-a-halftimes the weight of the fuel oil loaded.

For the combustion of a typical long-chain saturated hydrocarbon, theprocess balance between reactants and products is:

(CVH2.) + (3N/2) (02) - (N) (C02) + (N) (H20) EQN J-1

where:

CMH 2, - One mole of long-chain hydrocarbon.

02 -One mole of oxygen.

CO2 - One mole of carbon dioxide.

H20 - One mole of water.

N - A constant.

Equation J-1 shows that (3N/2) moles of oxygen are needed for thecombustion of one mole of fuel oil. Moles may be converted into weightsby the following relations:

3lement Molecular Weight

3 2C 120 32

J-1

-J 2-

One mole of C1Hl. weighs: NJ (12) + 2*(1] - 14N

3N/2 moles of 02 weigh: (3N/2) [(2)(16)) , 48N

4O3/14W = 3.428 a Relative weight of requ r"ed ozygento fuel.

The minimum weight of the oxygen is 3.428 times that of the fuel oil.Assuming that the amount of oxygen used in combustion is five-percentabove the amount needed for stoichiometric balance:

3.428 * 1.05 - 3.600 " Relative weLght of loaded oxygento fuel.

-Ki-

APPENDIX K: FACTORS AFFECTING CREW ENDURANCE

Some of the most important factors which affect crew enduranceare listed below, the factors can be grouped into two cate-gories: Vessel-related, and Personnel related.

1. Number of crewmembers, (complement).2. Quantity of provisions loaded.3. Fresh water tank capacity.4. Existence of fresh water distillers.5. Air purification capability and effectiveness.6. Space and volume per crewmember.

7. Quality of provisions loaded.8. Crew discipline and morale.9. Crew training state as individuals and as a team.10. Crewmember's ages.11. Crewmember's previous experience with similar situations.12. Crewmember's psychological profiles and temperament.

The focus of this study is necessarily directed to items (1)through (6). Hard data for the above factors is only availablewith consistency for item (1) in the literature, and even then,the sources often disagree. As such, much of the other data isgleaned from drawings that may be provided in the literature,with the author's best estimate of the unprovided data items.

-LI-

APPENDIX L: VULNERABILITY AND SURVIVABILITY FACTORS

Submarine vulnerability is directly proportional to its detect-ability of the submarine to acoustic, magnetic, thermal, andvisual sensors. The stealth capability of the submarine is itsgreatest asset as a military device, although it would be point-less militarily to build a submarine which was merely stealthy,without enough endurance to transit to where needed, enough sen-sor capability to be effective, and enough speed and weaponry toaccomplish its mission.

So, the idea, it would seem, is to build a submarine as invulner-able as possible, which means primarily as quiet as possible butalso encompasses the ability to defend itself or to escape inthe eventuality that it is detected.

Not all submarines have been designed to this philosophy. Somesubmarines seem to have been designed to withstand the damagefrom an attack, and continue. This is the concept of survivabi-lity. The U.S.S.R. in particular seems to have taken this ap-proach, with and perhaps not only for the purpose of survivingwartime attack, given the poor peacetime safety record of Sovietsubmarines, Reference (27).

Survivability may be improved by keeping these concepts inmind during the design of the submarine.

1. Redundant and separated vital systems and components:(a). MBT blow valves.(b). Propulsion motors.(c). Electric power cables.(d). Diesel generator sets.(e). Battery banks.

2. Strength and toughness of hull material.3. Using double-hull design.4. Dividing the pressure hull into watertight compartments.5. Using fire-resistant materials within the submarine.6. Adequate and appropriate fire-extinguishing gear.7. High state of crew training.8. High state of equipment readiness.9. Emergency air-breathing apparatus.

Finally, there is the issue of crew survivability and escape inthe event that the submarine is sunk. In several instances, thecrew would be unable to survive attacks severe enough to sinktheir submarine. The humane approach is certainly to provide thecrew with an escape pod, in the event its use becomes neccessary.Still, some countries prefer not to have an escape pod mounted,due to thier philosophy that the crew will perform more vigorouslyif the submarine itself is the only ticket home, Reference (15).

L-1

APPENDIX M: ESTIMATION OF HOTEL ELECTRIC LOAD

The open literature gives no empirical formulas for hotel elec-tric load. The following relation is the author's best attemptto parameterize this item which is an important factor in the en-durance calculations, primarily so that the hotel load of eachsubmarine is calculated by the same formula, rather than someequally arbitrary but non-uniform basis.

Lh = 1.5(Vmob) + 4(Vc3i) + 1.5(Vss) + l(Vwep) EQN M-1

where:Lh = Hotel electric load, KW.Vmob = Volume of the mobility machinery, cu ft.Vc3i = Volume of C31 equipment spaces, cu ft.Vss - Volume of ship support spaces, cu ft.Vwep = Volume of weapons spaces, cu ft.

M-1

APPENDIX N: DIESEL ENGINE DATA

The power output of each submarine's prime mover (diesel engine/alternator set, except for RUBIS) is of great importance in thecalculation of sustained maximum speed while surfaced or snorkel-ing, and in the calculation of the indiscretion rate. The poweroutput of the main propulsion electric motor used in each submar-ine is important in the calculation of maximum submerged speed.

The open-literature data on the diesel engines and main-propul-sion motors is listed in Table Ni.

N-i

-N 2-

SUBMARINE NAME

PRIME MOVER KILO WALRUS RUBIS BARBEL TYPEDATA 2400

MANUFACTURER MINISTRY OF SEMT- COMMISSARIAT FAIRBANKS- PAXMAN-SHIPBUILDNG PIELSTICK a L'ENERGIE MORSE VALENTA

ATOMIQUE

MODEL M50? PA4-V200-VG 38D8 RPA 200SZBHP, (EACH) 3000? 2310 -64,000 MAX 1600 1800

CYCLE 4 4 N/A 2 4CYLYNDERS 12V 12V (NUCLEAR 8 INLINE 16

SPEED, rpm 1700 1500 REACTOR) 900?SUPERCHRGING ? COMBINED N/A MECHANICAL? MECHANICALNUMBER ABOARD 2 3 1 3 2

........................................................................MOTOR MFGR: (U.S.S.R.) HOLEC JEU-SCHNDR 3E GECMOTOR KW "3000 4050 7500 2350 4100REFERENCE (11,17) (5,6,16,21) (9,10,21) (11,17) (5,6,10)

SUBMARINE NAME

PRIME MOVER TYPE TYPE SAURO VASTER- MIDGETDATA 1700 2000 GOTLAND I JO

MANUFACTURER MTU MTU GMT HEDEMORA SSOSVERKSTADER

MODEL 16V-652-MB8 7 A210 16M VRA/1546BHP, (EACH) 1475 1200 965 ? 420

CYCLE 4 4? 4? ?CYLYNDERS 16 16? 16 ? ?

SPEED, rpm ? ?SUPERCHRGING TURBO? TURBO? TURBO TURBO 7NUMBER ABOARD 4 4 3 2 1...... ................ .. ............ ............MOTOR MFGR: SIEMENS SIEMENS MCPN JEU-SCHNDR (DIESEL ISMOTOR KW 6600 5500 3200 ANAEROBIC)REFERENCE (5,6,15,21) (5,21) (5,6) (6,15,36) (6,29)

TABLE NI: Diesel engire and electri,- propulsion motor data.

Abbreviations:

GE - Gerral Electric.GMT - Grandi Motori Trieste.JEU-SCHNDR - Jeumont-Schneider.MTU- Motoren-und Turbinen-Union Friedrichshafen G.m.b.H.SSOS - Sub Sea Oil Services of Mi,-operi S.p.A.

-01 -

APPENDIX 0: DATA ON OTHER MODERN SUBMARINES

The literature contained information on several other submarineswhich were not included in the detailed study. The informationshown in Table 01 is taken primarily from References (5), (6),(7), and (17). The individual data entries are not attributedto the specific reference since most entries could be susbstan-tiated by multiple references.

0-1

DISPLACEMENTS DIMENSIONS-----------------------------------------------------------------------

SUBMARINE STAND SURFACE SUBSURF DRAFT DIAM LOANAME (Lton) (Lton) (Lton) (ft) (ft) (ft)

Federal Republic of GermanyTYPE 205 ? 419 450 14.1 15.1 144MSV 130 130 ? 8.856 9.84 85.608TR 1000 1000 ? ? 16.4 17.384 196.8TYPE 206 ? 450 498 14.8 15.1 159.4TR 1700 1760 2140 2350 21.32 24.6 216.5

FranceRUBIS 2250 2385 2670 21 24.9 236.5AGOSTA 1250 1510 1760 17.7 22.3 221.7DAPHNE ? 860 1038 15.1 22.3 189.6NARVAL ? 1635 1910 18 23.6 255.8

ItalyMIDGET 100 100 ? 136 8.5 10 89SAURO 1280 1480 1660 21 28.9 211.2-----------------------------------------------------------------------

The NetherlandsWALRUS 1900 2450 2800 21.6 27.6 223.1

MORAY 1400 1150 1310 1450 ? 21 177.1

SwedenVASTERGOTLAND 990 1070 1140 20 20 159.1NACKEN, (A14) ? 1030 1125 18.4 18.4 162.4SJOORMEN ? 1075 1400 19 20 167.3

Union of Soviet Socialist RepublicsFOXTROT 1500 1950 2500 20 26.2 300.1ZULU IV 1550 1950 2300 20 24.3 295.2ROMEO 1200 1400 1800 18 23.9 251.9WHISKEY 800 1080 1350 16.1 21.3 249.3KILO 1900 2500 3200 23 29.5 229.6

United KingdomTRAFALGAR ? 4000 5208 26.9 32.1 280.1SWIFTSURE 4000 4500 27 32.3 272OBERON 2030 2230 2455 18 26.5 295.2TYPE 2400 1850 2160 2400 17.7 25 230.6

United States of AmericaDARTER ? 1720 2388 19 27.2 284.5DOLPHIN 800 930 18 19.3 152BARBEL 2146 2315 2639 28 29 219.1

Table 01: Data on several other modern submarines, from the literature.(Sheet one of five).

SPEED PROPULSION PLANT

PRPULSION NUMBERSUBMARINE SUBSURF SURFACE SNORKEL PLANT OF PROPELLER

NAME (Kts) (Kts) (Kts) TYPE SHAFTS BLADES

Federal Republic of GermanyTYPE 205 17 10 ? D/E 1MSV 130 11 8 ? D/E 1 TR 1000 20 11 10 D/E 1 ?TYPE 206 17 10 ? D/E 1 ?TR 1700 25 13 15 D/E 1 7?

FranceRUBIS 25 20 N/A NUC/LQMTL 1 7AGOSTA 20 11 10 D/E 1 5DAPHNE 16 13.5 ? D/E 2 ?NARVAL 18 15 D/E 2 '

ItalyMIDGET 100 16 8 N/A D/E 1 7SAURO 19.3 11 11 D/E 1 7

The NetherlandsWALRUS 20 12 12 D/E 1 5MORAY 1400 20 12 12 D/E 1 5

SwedenVASTERGOTLAND 20 11 10 D/E 1 5NACKEN 20 20 ? D/E 1 5SJOORMEN 20 15 ? D/E 1 5?

Union of Soviet Socialist RepublicsFOXTROT 16 18 D/E 3ZULU IV 16 18 2 D/E 3 ?ROMEO 14 17 ? D/E 2WHISKEY 14 18 ? D/E 2 ?KILO 16 12 10 D/E 1 6

United KingdomTRAFALGAR 32 0 NUC/PWTR 1 7SWIFTSURE 30 0 NUC/PWTR 1OBERON 17 12 ? D/E 2 7TYPE 2400 20 12 D/E 1 7

United States of AmericaDARTER 19.5 14 ? D/E 2 7DOLPHIN 0 15 ? D/E 1BARBEL 21 15 10 D/E 1 ?

Table 01: Data on several other modern submarines, from the literature.(Sheet two cif five).

PROPULSION PLANT CAPACITIES

PRPULSION DIESEL ALTER- EMERG BATTERY NUMBERSUBMARINE MOTOR POWER NATOR MOTOR WEIGHT BATTERY

NAME (HP) (HP) (KW) (HP) (Lton) CELLS

Federal Republic of GermanyTYPE 205 500 1200 900 ? ? ?MSV 130 7 ? ? 18TR 1000 ? ? ? ? ? ?TYPE 206 800 1500 1150 ?'TR 1700 8844 6000 4400 N/A 518 980

FranceRUBIS 10000 N/A 10500 YES N/A N/AAGOSTA 4500 3600 2700 ? 185 320DAPHNE 2600 1224 900 "NARVAL 4800 .? "'

ItalyMIDGET 100 420 120 90 48 5.5 15?SAURO 3216 2894 2160 N/A ' 296

The NetherlandsWALRUS 5360 6930 5170 N/A 275 480MORAY 1400 Various Various Various ?

SwedenVASTERGOTLAND 2926 2680 2000 N/A 170 168NACKEN ? ? ? ?SJOORMEN ? 2200 1640 ? 7 7

Union of Soviet Socialist RepublicsFOXTROT 5500 6000 4500 .ZULU IV 5500 6000 4500 7 ?ROMEO 4000 4000 3000WHISKEY 2700 4000 3000 ? ? ?KILO 4000 6000 4500 ? 275? 480?

United KingdomTRAFALGAR 15000 4000 3000 ? ? ?SWIFTSURE 15000 4000 3000 7OBERON 6000 3680 2740 7 275 480TYPE 240o 5400 3618 2500 N/A 275 480

United States of AmericaDARTER 5500 4500 3375 .DOLPHIN 650 1650 1200 . ?BARBEL 3150 4800 3580 N/A 290 504

Table 01: Data on several other modern submarines, from the literature.(Sheet three o:f five).

RANGE AND DEPTH CAPABILITIES MANNING

ENDURANCE BATTERY PROVISION DIVESUBMARINE RANGE RANGE ENDURANCE DEPTH COMPLMNT COMPLMNT

NAME (Nm) (Nm) (Days) (m) OFFICER ENLISTED

Federal Republic of GermanyTYPE 205 ? ? ? ? 4 18MSV 130 ? 14 130 5,(+8) 0TR 1000 ? ? 40 ? 21 TOTAL -

TYPE 206 ? ? 150 4 18TR 1700 12000+ "450 70 300 8 22

FranceRUBIS ? ? 60 300 9 57AGOSTA 10500 350 65 250 4 45DAPHNE ? ?39NARVAL ? 56 7

ItalyMIDGET 100 1600 15 14 200 4 8SAURO 12500 7 45 300 7? 38?

The NetherlandsWALRUS 10000 200 @ 2 K 60-80 300 7 43MORAY 1400 9500 50 300 7 29

SwedenVASTERGOTLAND ? ? 30 300 7 13NACKEN . 7 7 21 TOTALSJOORMEN ? ? ? 23 TOTAL

Union of Soviet Socialist RepublicsFOXTROT . 75 TOTAL -

ZULU IV ? 75 TOTAL -ROMEO 9 7 " 55 TOTAL -WHISKEY 55 TOTAL -

KILO 80001? 45 300? 55 TOTAL -

United KingdomTRAFALGAR ? ? ? ? 12 85SWIFTSURE ? ? ? 12 85OBERON 12000 . 56 300 7 61TYPE 2400 7000+ 7 49 200 7 37

United States of AmericaDARTER ? ? ? 8 75DOLPHIN ? ? 7 15BARBEL ? 60 120'? 8 69

Table 01: Data on several other modern submarines, from the literature.(Sheet four of five).

41

WEAPONS SYSTEMS

SUBMARINE BOW DIAM OTHER RELOADS CRUISE MINENAME TUBES (in) TUBES CARRIED MISSILE? LAYING?

Federal Republic of GermanyTYPE 205 8 ? 0 8 ? ?MSV 130 0 ? 4,EXT 4 ?TR 1000 6 21? 0 6 NO? YES?TYPE 206 8 ? 0 8 ? ?TR 1700 6 21 0 22 NO YES?

FranceRUBIS 4 21 0 10 YES YESAGOSTA 4 21 0 16 YES YESDAPHNE 8 ? 4,S 12 ? ?NARVAL 6 ? 0 20 ? "?

ItalyMIDGET 100 4 15+ 0 4 NO YESSAURO 6 21+ 0 6 NO YES?

The NetherlandsWALRUS 4 21 0 20 YES YESMORAY 1400 6 21? 0 12 7 YES?

SwedenVASTERGOTLAND 4 21+ 3,15-in 6 NO YESNACKEN 6 21 2,15-in 8 NO YESSJOORMEN 4 ? 2,S 6 ?

Union of Soviet Socialist RepublicsFOXTROT 6 4,S 22 YES? YESZULU IV 6 ? 4,S 22 YES? YESROMEO 6 ? 2,S 14 YES? YESWHISKEY 4 7 2,S 12 YES? YESKILO 8 7 0 10 YES? YES

United KingdomTRAFALGAR 5 21 0 25 ? ?SWIFTSURE 5 21 0 25 .1

OBERON 6 21 2,S 14 ? YESTYPE 2400 6 21 0 18 YES YES

United States of AmericaDART1P 6 21 2,S 8 YES? YES?DOLPHIN 0 21 0 0 YES' YES?BARBEL 6 21 0 6 YES? YES?

Table 01: Data on several other modern submarines, from the literature.(Sheet five of five).

-P1-

APPENDIX P: DIESEL ENGINE SPECIFIC FUEL CONSUMPTION VARIABLES

The specific fuel consumption of modern diesel engines is in therange of approximately 0.30 to 0.35 lbs/HP-Hour, Reference (3).This exceptionally-low SFC is achieved when the engine is run onthe test stand, and under the "best" conditions of engine speedand power loading. For other speeds and other power loadings,the SFC is generally greater than this value. The SFC at the ac-tual condition of loading may be approximated graphically by thegeneric diagram of Figure P-1. Figure P-1 shows that the SFC willincrease at power levels other than approximately the 90% powerlevel, ana will also increase at engine RPM other than the approx-imate optimum of 90% of rated maximum RPM.

The specific fuel consumption of the installed diesel engines,while snorkeling, will be greater still than the values predic-ted by Figure P-l, because of.flow resistance in the snorkel in-take and uptake.

For the anaerobic diesel engines in the MIDGET 100, the exact SFCunder any conditions is not known, since Sub Sea Oil Services hasnot published the details of their technology. It is reasonableto assume that the SFC of the anaerobic diesel cycle, as a whole,is greater than that of a comparable conventional diesel cycle,since the carbon-dioxide exhaust gas produced, (after any startuptransients) must be discharged overboard at ambient pressure.

If the assumption is made that the operators of the diesel enginewill operate the engine at the optimum engine speed/power point,then the specific fuel consumption of the installed marine dieselengines, as described by Figure P-l, may be approximated by thefollowing:

SFC = 0.40 + 0.30(BHP90% - BHPop)/(0.65*BHPr) EQN P-1

where:SFC - Specific fuel consumption at the actual operating

point, lbs/HP-Hr.BHP90 - The power output of the engine at its assumed

optimum efficiency operating point: 90% of ratedpower, HP.

BHPop - The power output of the actual operating point,HP.

BHPr - The rated power output of the engine, HP.

Assumed values of the SFC for each engine, calculated fromEquation P-l, are listed in table P1.

P-1

-P2-

j00f

IIO

6AJFL/ P-rrE

fr~Fk ~4e'" 6).7

-P3-

SUBMARINE NAME

SFC AT SPEED KILO WALRUS RUBIS BARBEL TYPE(ESTIMATED) 2400

NMBR DIESELS 2 3 1 3 2FOR SINGLE DIESEL

FULL LOAD BHP 3000 2310 500 1600 180090% LOAD BHP 2700 2079 450 1440 1620

SPEED, Kts SFC = 0.35 + 0.3*@ABS(BHP.90 - BHPop)/(0.65*BHP FULL)2 0.737307 0.730694 0.599248 0.727355 0.724002

2.5 0.736386 0.729522 0.594114 0.725940 0.7225843 0.735034 0.727799 0.586574 0.723865 0.720500

3.5 0.733172 0.725423 0.576186 0.721008 0.7176284 0.730721 0.722295 0.562513 0.717250 0.713846

4.25 0.729250 0.720417 0.554308 0.714996 0.7115764.5 0.727603 0.718314 0.545119 0.712473 0.7090344.75 0.725769 0.715972 0.534891 0.709665 0.706204

5 0.723740 0.713380 0.523573 0.706559 0.7030715.25 0.721506 0.710525 0.511109 0.703139 0.6996215.5 0.719057 0.707395 0.497446 0.699391 0.695839

6 0.713477 0.700262 0.466314 0.690854 0.6872206.5 0.706924 0.691882 0.429752 0.680832 0.677096

7 0.699322 0.682158 0.387338 0.669211 0.6653497.5 0.690596 0.670993 0.655876 0.651863

8 0.680672 0.658291 0.640714 0.6365228.5 0.669475 0.643957 0.623611 0.619210

9 0.656930 0.627893 0.604455 0.59981110 0.627500 0.590198 0.559534 0.55429411 0.54444512 0.489877131415

Table PI: Estimated diesel engine specific fuel consumption, as afunction of speed. This calculation assumes the specificfuel consumption dependency with engine loading of EquationP-1, that the battery is not being charged, and that thediesel is supplying power for propulsion and hotelelectricity. (Sheet one of two).

-P4-

SUBMARINE NAME

SFC AT SPEED TYPE TYPE SAURO VASTER- MIDGET(ESTIMATED) 1700 2000 GOTLAND 100

NMBR DIESELS 4 4 3 2 2FOR SINGLE DIESEL

FULL LOAD BHP 1475 1200 965 1340 42090% LOAD BHP 1327.5 1080 868.5 1206 378

SPEED, Kts (NOTE 1)2 0.715395 0.707799 0.706846 0.734831 0.7423622 0.713772 0.706140 0.704970 0.733858 0.7415132 0.711391 0.703709 0.702217 0.732434 0.7402712 0.708112 0.700367 0.698428 0.730475 0.7385632 0.703796 0.695975 0.693444 0.727903 0.7363202 0.701206 0.693342 0.690454 0.726361 0.7349772 0.698307 0.690396 0.687106 0.724635 0.7334732 0.695080 0.687119 0.683381 0.722716 0.7318012 0.691509 0.683494 0.679259 0.720594 0.7299512 0.687577 0.679504 0.674722 0.718258 0.7279162 0.683267 0.675134 0.669749 0.715699 0.7256882 0.673449 0.665182 0.658421 0.709874 0.7206132 0.661919 0.653506 0.645121 0.703041 0.7146612 0.648546 0.639972 0.629698 0.695121 0.7077652 0.633197 0.624449 0.612001 0.686039 0.6998562 0.615742 0.606807 0.591876 0.675718 0.6908692 0.596049 0.586914 0.569176 0.664081 0.6807372 0.573987 0.564641 0.543749 0.651053 0.6693952 0.522239 0.512437 0.484118 0.620522 0.642817

11 0.459461 0.449164 0.411795 0.61061212 0.384624 0.373798 0.57226113 0.403297 0.414677 0.52724814 0.505325 0.517277 0.47505915 0.622475 0.635009 0.415182

Table P1: Estimated diesel engine specific fuel consumption, as afunction of speed. This calculation assumes the specificfuel consumption dependency with engine loading of EquationP-1, that the battery is not being charged, and that thediesel is supplying power for propulsion and hotelelectricity. NOTE: For MIDGET 100, the diesel is providingpropulsive power only. (Sheet two of two).

-Qi-

APPENDIX Q: CALCULATION OF PROVISIONING ENDURANCE

The provision endurance range is based primarily upon the food-stores loadout for the crew. It is a linear function with speed,being directly proportional to the speed. For this reason, theactual endurance range of a submarine may be far less than hadbeen calculated from the consideration of the bunker fuel loadoutalone. At low speeds, the submarine range is limited by the load-out of foodstores, since those are exhausted prior to the exhaus-tion of bunker fuel.

The provisioning endurance range may be expressed as:

Mpr - (#P)(V)(24) EQN Q-1

where:Mpr - Endurance range based on provisions, Nm.#P - Number of days of provision loadout.V - Speed of travel, Kts.24 - Conversion factor, hours/day.

The comparison of fuel endurance range to provision endurancerange is shown in Figures in Chapter X.

Q- 1

-Q2-

PROVISIONING KILO WALRUS RUBIS BARBEL TYPE

ENDURANCE 2400

SPEED, Kts PROVISIONING ENDURANCE, Nm2 2160 3360 2880 2880 2352

2.5 2700 4200 3600 3600 2940

3 3240 5040 4320 4320 3528

3.5 3780 5880 5040 5040 4116

4 4320 6720 5760 5760 4704

4.25 4590 7140 6120 6120 4998

4.5 4860 7560 6480 6480 5292

4.75 5130 7980 6840 6840 55865 5400 8400 7200 7200 5880

5.25 5670 8820 7560 7560 61745.5 5940 9240 7920 7920 6468

6 6480 10080 8640 8640 70566.5 7020 10920 9360 9360 7644

7 7560 11760 10080 10080 8232

7.5 8100 12600 10800 10800 8820

8 8640 13440 11520 11520 9408

8.5 9180 14280 12240 12240 9996

9 9720 15120 12960 12960 10584

10 10800 16800 14400 14400 11760---------------------------------------------------------------------------

PROVISIONING TYPE TYPE SAURO VASTER- MIDGET

ENDURANCE 1700 2000 GOTL'D 100---------------------------------------------------------------------------

SPEED, Kts PROVISIONING ENDURANCE, Nm2 3360 4320 2160 1440 672

2.5 4200 5400 2700 1800 840

3 5040 6480 3240 2160 1008

3.5 5880 7560 3780 2520 11764 6720 8640 4320 2880 1344

4.25 7140 9180 4590 3060 1428

4.5 7560 9720 4860 3240 1512

4.75 7980 10260 5130 3420 1596

5 8400 10800 5400 3600 1680

5.25 8820 11340 5670 3780 1764

5.5 9240 11880 5940 3960 1848

6 10080 12960 6480 4320 2016

6.5 10920 14040 7020 4680 21847 11760 15120 7560 5040 2352

7.5 12600 16200 8100 5400 25208 13440 17280 8640 5760 2688

8.5 14280 18360 9180 6120 28569 15120 19440 9720 6480 3024

10 16800 21600 I0800 7200 3360

Table 01: Provisonling endurance, in nautical miles, at various speeds.

-R1-

APPENDIX R: ESTIMATION OF PRISMATIC COEFFICIENT

The prismatic coefficient of each submarine is found by firstcalculating the envelope volume, which will have tha dispalcementof the submarine while submerged, plus free flood, which may beassumed to be approximately five percent. The volume s of theappendages and sail are then estimated from pictures in the lit-erature, and are subtracted from the envelope volume. The resultof this calculation is the bare-hull volume.

The ratio of the volume of the bare hull to the volume describedby the product of the maximum section area and the length overallis the prismatic coefficient.

The calculated values for prismatic coefficient are shown inTable R1.

R-1

-R2-

SUBMARINE NAME

PRISMATIC KILO WALRUS RUBIS BARBEL TYPECOEFFICIENT, Cp REF REF REF REF 2400 REF

LENGTH, (f t) 229.6 (17) 223.1 (23) 236.5 219.1 (17) 230.6 (32)BEAN, (f t) 29.5 (17) 27.6 (23) 24.9 29 (17) 25 (32)

TOTAL ENVLPE VOL 117600 102900 98122 96983 88200(MINUS) SAIL VOL -1500 (e) -1273 -2037 -1900 -2460MINUS APPDGE VOL -200 (e) -118 -220 -230 -240BAREHULL ENV VOL 115900 101509 95865 94853 85500PRISMATIC COEFF. 0.738 0.760 0.832 0.655 0.755L/D RATIO: 7.783 8.083 9.497 7.555 9.224

HULL SURF AREA 18000 (e) 16705 17039 15436 16316Cws 0.845 0.863 0.921 0.773 0.900

REFERENCE DRAWINGFOR MEASUREMENTS: (e) (18) (10) (35) (13)


LENGTH, (f t) 216.5 (7) 210.6 (6) 211.2 159.1 88.9BEAM, (f t) 23.9 (7) 24.4 (6) 22.3 20.3 10.3

TOTAL ENVLPE VOL 86362 85628 61005 41895 4998(MINUS) SAIL VOL -2200 -1232 -1450 -960 -160MINUS APPDGE VOL -155 -215 -154 -50 -37BAREHULL ENV VOL 84007 84181 59401 40885 4801PRISMATIC COEFF. 0.864 0.854 0.720 0.793 0.648L/D RATIO: 9.058 8.631 9.386 7.837 8.631

HULL SURF AREA 15903 14656 12383 9150 2267Cws 0.978 0.907 0.829 0.901 0.788

REFERENCE DRAWINGFOR MEASUREMENTS: (2) (e) (12) (36) (29)

Table R-1: Calculation of prismatic coefficient.

Documents

Comparative Naval Architecture of Modern Foreign Submarines